A368760 a(n) = n! * (1 + Sum_{k=0..n} k^3 / k!).
1, 2, 12, 63, 316, 1705, 10446, 73465, 588232, 5294817, 52949170, 582442201, 6989308140, 90861008017, 1272054114982, 19080811728105, 305292987653776, 5189980790119105, 93419654222149722, 1774973430220851577, 35499468604417039540, 745488840692757839601
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Bell Polynomial.
- Wikipedia, Touchard polynomials.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace((1+sum(k=0, 3, stirling(3, k, 2)*x^k)*exp(x))/(1-x)))
Formula
a(0) = 1; a(n) = n*a(n-1) + n^3.
a(n) = n! + A337001(n).
E.g.f.: (1 + B_3(x) * exp(x)) / (1-x), where B_n(x) = Bell polynomials.