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Expansion of e.g.f. exp(1 - (1+x)^5).
2

%I #11 Jan 31 2024 08:06:17

%S 1,-5,5,115,-95,-8245,-21275,896275,8801825,-95466725,-2703832475,

%T -3522650125,717727962625,9961465952875,-118944021914875,

%U -5634631318806125,-37511809003469375,2020875725751906875,55489065505990733125,-65182838564153418125

%N Expansion of e.g.f. exp(1 - (1+x)^5).

%F a(0) = 1; a(n) = -5 * (n-1)! * Sum_{k=1..min(5,n)} binomial(4,k-1) * a(n-k)/(n-k)!.

%F a(n) = Sum_{k=0..n} 5^k * Stirling1(n,k) * A000587(k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)^5)))

%Y Column k=5 of A369738.

%Y Cf. A000587, A202825.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jan 30 2024