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 A368576 a(n) = n! * Sum_{k=0..n} binomial(k+4,5) / k!. 3
 0, 1, 8, 45, 236, 1306, 8088, 57078, 457416, 4118031, 41182312, 453008435, 5436105588, 70669378832, 989371312216, 14840569694868, 237449115133392, 4036634957288013, 72659429231210568, 1380529155393034441, 27610583107860731324, 579822245265075410934 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..21. FORMULA a(0) = 0; a(n) = n*a(n-1) + binomial(n+4,5). E.g.f.: x * (1+2*x+x^2+x^3/6+x^4/120) * exp(x) / (1-x). PROG (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 4, binomial(4, k)*x^k/(k+1)!)*exp(x)/(1-x)))) CROSSREFS Cf. A007526, A103519, A368574, A368575. Cf. A000389. Sequence in context: A297089 A032208 A163003 * A055422 A204618 A289896 Adjacent sequences: A368573 A368574 A368575 * A368577 A368578 A368579 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Dec 31 2023 STATUS approved

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Last modified May 18 11:53 EDT 2024. Contains 372630 sequences. (Running on oeis4.)