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A007611
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a(n) = n! + 2^n.
(Formerly M0807)
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7
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2, 3, 6, 14, 40, 152, 784, 5168, 40576, 363392, 3629824, 39918848, 479005696, 6227028992, 87178307584, 1307674400768, 20922789953536, 355687428227072, 6402373705990144, 121645100409356288, 2432902008177688576
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Answer to the problem A1 proposed during the 51th Putnam Competition in 1990 (see Kedlaya and Larson links). - Bernard Schott, Mar 29 2023
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REFERENCES
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Ron Larson, Robert P. Hostetler and Bruce H. Edwards, Exercise 135 in Calculus of a Single Variable for Advanced High School Students, Page 605, 8th Edition, 2006.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Kiran S. Kedlaya, Problem A-1, The 51th William Lowell Putnam Mathematical Competition, Dec 08 1990.
Loren Larson, Problem A-1, 51st Annual Putnam Competition, Math. Mag., 64 (1991), 141-144.
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FORMULA
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a(n) = (n+4)*a(n-1) - 4*n*a(n-2) + (4*n-8)*a(n-3) with a(0) = 2, a(1) = 3, a(2) = 6. - Dennis S. Kluk (mathemagician(AT)ameritech.net), Feb 12 2006
E.g.f.: 1/(1-x) + exp(2x). (End)
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [factorial(n)+2^n for n in range(0, 21)] # Zerinvary Lajos, Oct 27 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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