A361828 a(0) = 1; a(n+1) = Sum_{k=0..n} k^k * a(n-k).

1, 1, 2, 7, 40, 338, 3841, 54821, 939335, 18744832, 426390069, 10881017916, 307686450208, 9546443638409, 322375619648549, 11769010007246745, 461834905502223078, 19384809864763869231, 866564718107731746860, 41102477939620052536314

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: 1 / (1 - x * Sum_{k>=0} (k*x)^k).

a(n) ~ exp(-1) * n^(n-1). - Vaclav Kotesovec, Mar 26 2023

Mathematica

nmax = 20; CoefficientList[Series[1/(1 - x - x*Sum[(k*x)^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 26 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-x*(sum(k=0, N, (k*x)^k))))

Crossrefs

Cf. A000312, A051295, A277610.

Sequence in context: A135082 A372348 A102317 * A031973 A274279 A319945

Adjacent sequences: A361825 A361826 A361827 * A361829 A361830 A361831

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 26 2023

Status

approved