A344100 Expansion of Product_{k>=1} (1 + x^k)^binomial(k+4,5).

1, 1, 6, 27, 92, 323, 1070, 3527, 11314, 35708, 110478, 336629, 1011097, 2997233, 8778761, 25424358, 72867447, 206804742, 581573340, 1621407554, 4483701126, 12303384015, 33514076529, 90656680725, 243603875523, 650444927010, 1726229294595, 4554686670838, 11950683658941

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: exp( Sum_{k>=1} (-1)^(k+1) * x^k / (k*(1 - x^k)^6) ).

Mathematica

nmax = 28; CoefficientList[Series[Product[(1 + x^k)^Binomial[k + 4, 5], {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[(-1)^(k/d + 1) d Binomial[d + 4, 5], {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 28}]

Crossrefs

Cf. A000389, A000417, A028377, A258343, A305206, A344099, A344101.

Sequence in context: A121596 A264026 A341385 * A136747 A278357 A001940

Adjacent sequences: A344097 A344098 A344099 * A344101 A344102 A344103

Keyword

nonn

Author

Ilya Gutkovskiy, May 09 2021

Status

approved