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a(n) = [x^n] 1/Sum_{k=0..n} k^k*x^k.
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%I #26 Feb 07 2020 20:50:04

%S 1,-1,-3,-20,-197,-2511,-38924,-708105,-14769175,-347328540,

%T -9093250277,-262350229095,-8271756463988,-283017783855881,

%U -10445207569804687,-413662097635230500,-17499340294430480565,-787591765696468470799,-37578217833375886576604

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

%C 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

%H Seiichi Manyama, <a href="/A296715/b296715.txt">Table of n, a(n) for n = 0..386</a>

%F a(0) = 1; a(n) = -Sum_{k=1..n} k^k * a(n-k). - _Ilya Gutkovskiy_, Feb 07 2020

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

%Y Cf. A000312, A167894, A296617, A316090.

%K sign

%O 0,3

%A _Seiichi Manyama_, Dec 19 2017