A296715 a(n) = [x^n] 1/Sum_{k=0..n} k^k*x^k.

1, -1, -3, -20, -197, -2511, -38924, -708105, -14769175, -347328540, -9093250277, -262350229095, -8271756463988, -283017783855881, -10445207569804687, -413662097635230500, -17499340294430480565, -787591765696468470799, -37578217833375886576604

Offset: 0

Author

Seiichi Manyama, Dec 19 2017

Keywords

• sign

Comments

A function f:[n]->[n] is decomposable if for some k < n, f([k]) is contained in [k] and f([n-k]) is contained in [n-k]. For n>=1, -a(n) is the number of functions f:[n]->[n] that are not decomposable. - Geoffrey Critzer, Oct 16 2018

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A000312, A167894, A296617, A316090.

Programs

PARI

N=66; x='x+O('x^N); Vec(1/sum(k=0, N, k^k*x^k))

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} k^k * a(n-k). - Ilya Gutkovskiy, Feb 07 2020