A357480 a(n) = (n!/24) * Sum_{k=0..n-4} 1/k!.
0, 0, 0, 0, 1, 10, 75, 560, 4550, 41076, 410970, 4521000, 54252495, 705283150, 9873965101, 148109477880, 2369751647900, 40285778016680, 725144004303300, 13777736081766576, 275554721635336365, 5786649154342069650, 127306281395525539615, 2928044472097087420000
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..450
Programs
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PARI
a(n) = n!/24*sum(k=0, n-4, 1/k!);
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PARI
a(n) = n!*sum(k=0, n, binomial(k, 4)/k!);
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PARI
my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(x^4/24*exp(x)/(1-x)))) -
PARI
my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=4, N, k!*x^k/(1-x)^(k+1))/24))
Formula
a(n) = n! * Sum_{k=0..n} binomial(k,4)/k!.
a(0) = 0; a(n) = n * a(n-1) + binomial(n,4).
E.g.f.: x^4/24 * exp(x)/(1-x).
G.f.: (1/24) * Sum_{k>=4} k! * x^k/(1-x)^(k+1).