A323634 Expansion of Product_{k>=1} 1/(1 - k^(k-1)*x^k).

1, 1, 3, 12, 80, 723, 8716, 128227, 2251086, 45647542, 1051845574, 27107414480, 772785074811, 24136982014698, 819697939365724, 30068912837398063, 1184872370227462528, 49914074776385885492, 2238476211786621770206, 106476394492364281869654, 5354276181476337307494676

Offset

0,3

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1, g(n) = n^(n-1). - Seiichi Manyama, Aug 22 2020

Links

Seiichi Manyama, Table of n, a(n) for n = 0..387

Formula

a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-2) + 3*exp(-1)/2)/n^2). - Vaclav Kotesovec, Jan 22 2019

Maple

a:=series(mul(1/(1-k^(k-1)*x^k), k=1..100), x=0, 21): seq(coeff(a, x, n), n=0..20); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1 - k^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d^(k - k/d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 20}]

Prog

(PARI) N=40; x='x+O('x^N); Vec(1/prod(k=1, N, 1-k^(k-1)*x^k)) \\ Seiichi Manyama, Aug 22 2020

Crossrefs

Cf. A023879, A023882, A266964, A299786, A300579.

Sequence in context: A213139 A023879 A084565 * A275488 A304561 A303227

Adjacent sequences: A323631 A323632 A323633 * A323635 A323636 A323637

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 21 2019

Status

approved