A299786 Expansion of Product_{k>=1} (1 + k^(k-1)*x^k).

1, 1, 2, 11, 73, 707, 8547, 127379, 2237804, 45511484, 1049155214, 27060763974, 771662014455, 24109614539775, 818906748562249, 30044648617150066, 1184045057676213763, 49883902402848781573, 2237286132689496359239, 106426356238092171308928, 5352031894869594850387969

Offset

0,3

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1, g(n) = (-1) * 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 + (2*exp(-2) + 3*exp(-1)/2)/n^2). - Vaclav Kotesovec, Jan 22 2019

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + k^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) 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(prod(k=1, N, 1+k^(k-1)*x^k)) \\ Seiichi Manyama, Aug 22 2020

Crossrefs

Cf. A265949, A266964, A304961, A321387, A323634.

Sequence in context: A323842 A049671 A074609 * A335310 A199417 A114179

Adjacent sequences: A299783 A299784 A299785 * A299787 A299788 A299789

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 21 2019

Status

approved