A297322 a(n) = [x^n] Product_{k>=1} (1 + k*x^k)^n.

1, 1, 5, 28, 137, 726, 3896, 21071, 115089, 633007, 3500740, 19448573, 108458924, 606787572, 3404112479, 19142919543, 107874784017, 609021410570, 3443952349385, 19503777943838, 110599636109572, 627924447630011, 3568885868192419, 20304321490356084

Offset: 0

Author

Ilya Gutkovskiy, Dec 28 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..1000

Crossrefs

Main diagonal of A297321.

Cf. A297324, A297326, A297329.

Programs

Maple

f:= proc(n) local k;
coeff(series(mul((1+k*x^k)^n,k=1..n),x,n+1),x,n);
end proc:
map(f, [$0..30]); # Robert Israel, Dec 28 2017

Mathematica

Table[SeriesCoefficient[Product[(1 + k x^k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 24}]

Formula

a(n) = A297321(n,n).

a(n) ~ c * d^n / sqrt(n), where d = 5.814548482877687529318372516965305077397562... and c = 0.2563102401728134539247148322678842806264... - Vaclav Kotesovec, Aug 01 2019