A196834 Row sums of Sheffer triangle A193685 (5-restricted Stirling2 numbers).

1, 6, 37, 235, 1540, 10427, 73013, 529032, 3967195, 30785747, 247126450, 2050937445, 17585497797, 155666739742, 1421428484337, 13377704321695, 129659127547372, 1293095848212799, 13259069937250169, 139671750579429512, 1510382932875294447, 16754464511605466311

Offset: 0

Author

Wolfdieter Lang, Oct 07 2011

Keywords

• nonn
• easy

Examples

			a(2) = 25 + 11 + 1 = 37.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000110, A005493, A005494, A045379, A196835 (alternating row sums).

Programs

Maple

b:= proc(n, m) option remember;
     `if`(n=0, 1, m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 5):
seq(a(n), n=0..23);  # Alois P. Heinz, Aug 22 2021

Mathematica

nmax = 20; CoefficientList[Series[E^(E^x + 5*x - 1), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 10 2020 *)

Formula

a(n) = Sum_{m=0..n} A193685(n,m).

E.g.f.: exp(exp(x)+5*x-1).

a(n) ~ exp(n/LambertW(n) - n - 1) * n^(n + 5) / LambertW(n)^(n + 11/2). - Vaclav Kotesovec, Jun 10 2020

a(0) = 1; a(n) = 5 * a(n-1) + Sum_{k=0..n-1} binomial(n-1,k) * a(k). - Ilya Gutkovskiy, Jul 03 2020