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

0,2

Links

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A081188 A218186 A154623 * A005389 A080954 A271905

Adjacent sequences: A196831 A196832 A196833 * A196835 A196836 A196837

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 07 2011

Status

approved