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URL: https://oeis.org/A097821

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A097821
Expansion of e.g.f. exp(2x)/(1-5x).
1
1, 7, 74, 1118, 22376, 559432, 16783024, 587405968, 23496238976, 1057330754432, 52866537722624, 2907659574746368, 174459574484786176, 11339872341511109632, 793791063905777690624, 59534329792933326829568
OFFSET
0,2
COMMENTS
Second binomial transform of n!*5^n.
LINKS
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
Sequence in context: A390311 A266305 A098118 * A337387 A054745 A323322
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 26 2004
STATUS
approved