A296617 -id:A296617 - cp's OEIS frontend

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

Seiichi Manyama, Dec 19 2017

sign

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

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

Cf. A000312, A167894, A296617, A316090.

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

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

A294372 Expansion of (1-x)^4/(x^2 + 4*x + 1).

Original entry on oeis.org

1, -8, 37, -144, 540, -2016, 7524, -28080, 104796, -391104, 1459620, -5447376, 20329884, -75872160, 283158756, -1056762864, 3943892700, -14718807936, 54931339044, -205006548240, 765094853916, -2855372867424, 10656396615780, -39770213595696, 148424457767004

Offset: 0

Seiichi Manyama, Dec 19 2017

Seiichi Manyama, Table of n, a(n) for n = 0..1746
Index entries for linear recurrences with constant coefficients, signature (-4,-1).

Cf. A000578, A296617.

N=66; x='x+O('x^N); Vec((1-x)^4/(x^2+4*x+1))

G.f.: 1/Sum_{k>=0} (k+1)^3*x^k.
From Colin Barker, Dec 19 2017: (Start)
a(n) = -6*sqrt(3)*((-2-sqrt(3))^n*(-2+sqrt(3)) + (-2+sqrt(3))^n*(2+sqrt(3))) for n > 2.
a(n) = -4*a(n-1) - a(n-2) for n > 4.
(End)

cp's OEIS Frontend

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

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