A344098 a(n) = [x^n] Product_{k>=1} (1 + x^k)^binomial(k+n-1,n-1).

1, 1, 4, 29, 221, 2027, 21022, 242209, 3060262, 41936745, 618154670, 9735013136, 162892047930, 2882449728121, 53727527279464, 1051276401060921, 21529017626095851, 460231878244308738, 10246160509840187387, 237067632496414877363, 5689786581042000827057, 141415234722601777758232

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Mathematica

Table[SeriesCoefficient[Product[(1 + x^k)^Binomial[k + n - 1, n - 1], {k, 1, n}], {x, 0, n}], {n, 0, 21}]
A[n_, k_] := A[n, k] = If[n == 0, 1, (1/n) Sum[Sum[(-1)^(j/d + 1) d Binomial[d + k - 1, k - 1], {d, Divisors[j]}] A[n - j, k], {j, 1, n}]]; a[n_] := A[n, n]; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A075197, A209668, A219555, A305206, A338645, A343200, A344097.

Sequence in context: A281600 A135429 A079756 * A221415 A087809 A140526

Adjacent sequences: A344095 A344096 A344097 * A344099 A344100 A344101

Keyword

nonn

Author

Ilya Gutkovskiy, May 09 2021

Status

approved