OFFSET
0,2
COMMENTS
Second binomial transform of n!*5^n.
LINKS
Robert Israel, Table of n, a(n) for n = 0..353
FORMULA
a(n) = 5*n*a(n-1) + 2^n, n > 0, a(0)=1.
D-finite with recurrence a(n) +(-5*n-2)*a(n-1) +10*(n-1)*a(n-2)=0. - R. J. Mathar, Aug 20 2021
a(n) = 5^n * n! * Sum_{k = 0..n} (2/5)^k/k! = 5^n * exp(2/5) * gamma(n + 1, 2/5). - Gerry Martens, Nov 07 2022
MAPLE
f:= proc(n) option remember; 5*n*procname(n-1)+2^n end proc:
f(0):= 1:
map(f, [$0..50]); # Robert Israel, Nov 10 2022
PROG
(PARI) my(x='x + O('x^25)); Vec(serlaplace(exp(2*x)/(1-5*x))) \\ Michel Marcus, Nov 08 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 26 2004
STATUS
approved