A270367 a(n) = (n+1)!*Sum_{k=0..(n-1)/2}((k)!*stirling2(n-k,k+1)/(n-k)!/(k+1)).

0, 2, 3, 10, 35, 191, 1162, 8996, 77877, 786757, 8801276, 110180038, 1508049127, 22568091079, 364984569510, 6360525167496, 118634584548905, 2360362530705801, 49871009321693920, 1115567129580176010, 26332809559025886651

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: -(((x+1)*e^x-1)*log(-x*e^x+x+1))/(x*e^x-x).

a(n) ~ (n-1)! * (1 + 1/r + r) / r^n, where r = 0.8064659942363268087699282186454... is the root of the equation exp(r) = 1 + 1/r. - Vaclav Kotesovec, Mar 22 2016

Mathematica

Table[(n+1)! * Sum[k!*StirlingS2[n-k, k+1]/(n-k)!/(k+1), {k, 0, (n-1)/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 22 2016 *)

Prog

(Maxima)
makelist((n)!*coeff(taylor(-(((x+1)*%e^x-1)*log(-x*%e^x+x+1))/(x*%e^x-x), x, 0, 15), x, n), n, 0, 15);
a(n):=(n+1)!*sum((k)!*stirling2(n-k, k+1)/(n-k)!/(k+1), k, 0, (n-1)/2);

Crossrefs

Cf. A048993.

Sequence in context: A356926 A378730 A134959 * A056607 A278051 A060604

Adjacent sequences: A270364 A270365 A270366 * A270368 A270369 A270370

Keyword

nonn

Author

Vladimir Kruchinin, Mar 22 2016

Status

approved