A344101 Expansion of Product_{k>=1} (1 + x^k)^binomial(k+5,6).

1, 1, 7, 35, 133, 511, 1869, 6797, 24095, 83938, 286734, 964348, 3196984, 10460310, 33813984, 108076908, 341821250, 1070484009, 3321584021, 10217036263, 31169524988, 94351439060, 283498600776, 845848778722, 2506779443603, 7381617323598, 21603241378334, 62853440151768

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: exp( Sum_{k>=1} (-1)^(k+1) * x^k / (k*(1 - x^k)^7) ).

Mathematica

nmax = 27; CoefficientList[Series[Product[(1 + x^k)^Binomial[k + 5, 6], {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 + 5, 6], {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 27}]

Crossrefs

Cf. A000428, A000579, A028377, A258343, A305206, A344099, A344100.

Sequence in context: A327243 A059595 A327385 * A001941 A320050 A160460

Adjacent sequences: A344098 A344099 A344100 * A344102 A344103 A344104

Keyword

nonn

Author

Ilya Gutkovskiy, May 09 2021

Status

approved