OFFSET
0,3
COMMENTS
Previous name was: Row sums of triangle A075503 (for n>=1).
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..110
FORMULA
a(n) = Sum_{m=0..n} 8^(n-m)*S2(n,m), with S2(n,m) = A008277(n,m) (Stirling2).
E.g.f.: exp((exp(8*x)-1)/8).
O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 8*j*x). - Ilya Gutkovskiy, Mar 20 2018
a(n) ~ 8^n * n^n * exp(n/LambertW(8*n) - 1/8 - n) / (sqrt(1 + LambertW(8*n)) * LambertW(8*n)^n). - Vaclav Kotesovec, Jul 15 2021
MAPLE
[seq(factorial(k)*coeftayl(exp((exp(8*x)-1)/8), x = 0, k), k=0..20)]; # Muniru A Asiru, Mar 20 2018
MATHEMATICA
Table[8^n BellB[n, 1/8], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 20 2015 *)
PROG
(GAP) List([0..20], n->Sum([0..n], m->8^(n-m)*Stirling2(n, m))); # Muniru A Asiru, Mar 20 2018
CROSSREFS
KEYWORD
nonn,easy,eigen
AUTHOR
Wolfdieter Lang, Oct 02 2002
EXTENSIONS
a(0)=1 inserted and new name by Vladimir Reshetnikov, Oct 20 2015
STATUS
approved