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A368719
a(n) = n! * Sum_{k=0..n} k^5 / k!.
2
0, 1, 34, 345, 2404, 15145, 98646, 707329, 5691400, 51281649, 512916490, 5642242441, 67707158124, 880193426905, 12322708514494, 184840628476785, 2957450056677136, 50276650964931169, 904979717370650610, 17194614630044837689, 343892292600899953780
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
a(0) = 0; a(n) = n*a(n-1) + n^5.
E.g.f.: B_5(x) * exp(x) / (1-x), where B_n(x) = Bell polynomials.
a(n) ~ 52*exp(1)*n!. - Vaclav Kotesovec, Jan 13 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, 5, stirling(5, k, 2)*x^k)*exp(x)/(1-x))))
CROSSREFS
Column k=5 of A337085.
Sequence in context: A251938 A059338 A301954 * A362953 A244881 A296833
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 04 2024
STATUS
approved