(Translated by https://www.hiragana.jp/)
A138523 - OEIS
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A138523
a(n) = Sum_{k=1..n} (2k-1)!.
4
1, 7, 127, 5167, 368047, 40284847, 6267305647, 1313941673647, 357001369769647, 122002101778601647, 51212944273488041647, 25903229683158464681647, 15537113273014144448681647, 10904406563691366305216681647, 8852666400303393320848832681647, 8231691320578226211046411712681647
OFFSET
1,2
COMMENTS
a(n) is divisible by 107 for n >= 53. - Robert Israel, Dec 01 2015
Last digit is 7 for n > 1. Therefore there is no square in this sequence except 1. - Altug Alkan, Dec 01 2015
a(n) is the rank of [2,1, 4,3, ..., 2n,2n-1] within the permutations of [1, 2, ... 2n-1, 2n] in lexicographic order. See A375302 for the ranking function. - Hugo Pfoertner, Aug 25 2024
LINKS
FORMULA
Recurrence: a(1) = 1, a(2) = 7, a(n) = (4*n^2-6*n+3)*a(n-1) - 2*(n-1)*(2*n-1)*a(n-2). - Vladimir Reshetnikov, Oct 28 2015
MAPLE
a:=proc(n) options operator, arrow: sum(factorial(2*k-1), k=1..n) end proc: seq(a(n), n=1..14); # Emeric Deutsch, Mar 31 2008
MATHEMATICA
Table[Sum[(2i - 1)!, {i, n}], {n, 15}] (* Stefan Steinerberger, Mar 25 2008 *)
PROG
(PARI) a(n) = sum(k=1, n, (2*k-1)!); \\ Michel Marcus, Oct 28 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Mar 23 2008
EXTENSIONS
More terms from Stefan Steinerberger, Emeric Deutsch and Robert G. Wilson v, Mar 25 2008
STATUS
approved