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A196834 Row sums of Sheffer triangle A193685 (5-restricted Stirling2 numbers). 5
1, 6, 37, 235, 1540, 10427, 73013, 529032, 3967195, 30785747, 247126450, 2050937445, 17585497797, 155666739742, 1421428484337, 13377704321695, 129659127547372, 1293095848212799, 13259069937250169, 139671750579429512 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)