OFFSET
0,3
COMMENTS
Previous name was: Row sums of triangle A075502 (for n>=1).
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..110
FORMULA
a(n) = sum((7^(n-m))*S2(n,m), m=0..n), with S2(n,m) = A008277(n,m) (Stirling2).
E.g.f.: exp((exp(7*x)-1)/7).
O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 7*j*x). - Ilya Gutkovskiy, Mar 20 2018
a(n) ~ 7^n * n^n * exp(n/LambertW(7*n) - 1/7 - n) / (sqrt(1 + LambertW(7*n)) * LambertW(7*n)^n). - Vaclav Kotesovec, Jul 15 2021
MAPLE
[seq(factorial(k)*coeftayl(exp((exp(7*x)-1)/7), x = 0, k), k=0..20)]; # Muniru A Asiru, Mar 20 2018
MATHEMATICA
Table[7^n BellB[n, 1/7], {n, 0, 20}]
PROG
(GAP) List([0..20], n->Sum([0..n], m->7^(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