(Translated by https://www.hiragana.jp/)
A078124 - OEIS
login
A078124
Second column, M(n+1,1) for n>=0, of infinite lower triangular matrix M defined in A078122.
17
1, 3, 12, 93, 1632, 68457, 7112055, 1879090014, 1287814075131, 2325758241901161, 11213788533232011006, 145939965725683888932081, 5174322925070232320838406581, 503750821963423009552527526376232
OFFSET
0,2
LINKS
FORMULA
The partitions of 2*3^n into powers of 3, or, the coefficient of x^(2*3^n) in 1/Product_{j=0..inf}(1-x^(3^j)) (conjecture).
EXAMPLE
a(1)=3 since the coefficient of x^6 in 1/Product_{j=0..inf}(1-x^(3^j)) = 1 + x + x^2 + 2x^3 + 2x^4 + 2x^5 + 3x^6 + ... is 3.
MATHEMATICA
m[i_, j_] := m[i, j]=If[j==0||i==j, 1, m3[i-1, j-1]]; m2[i_, j_] := m2[i, j]=Sum[m[i, k]m[k, j], {k, j, i}]; m3[i_, j_] := m3[i, j]=Sum[m[i, k]m2[k, j], {k, j, i}]; a[n_] := m[n+1, 1]
CROSSREFS
Cf. A078121, A078122 (matrix shift when cubed), A078123, A078125.
Sequence in context: A363254 A368454 A263801 * A115245 A145074 A374582
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 18 2002
STATUS
approved