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%I #17 Dec 20 2022 12:04:30
%S 1,7,74,1118,22376,559432,16783024,587405968,23496238976,
%T 1057330754432,52866537722624,2907659574746368,174459574484786176,
%U 11339872341511109632,793791063905777690624,59534329792933326829568
%N Expansion of e.g.f. exp(2x)/(1-5x).
%C Second binomial transform of n!*5^n.
%H Robert Israel, <a href="/A097821/b097821.txt">Table of n, a(n) for n = 0..353</a>
%F a(n) = 5*n*a(n-1) + 2^n, n > 0, a(0)=1.
%F 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
%F 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
%p f:= proc(n) option remember; 5*n*procname(n-1)+2^n end proc:
%p f(0):= 1:
%p map(f, [$0..50]); # _Robert Israel_, Nov 10 2022
%o (PARI) my(x='x + O('x^25)); Vec(serlaplace(exp(2*x)/(1-5*x))) \\ _Michel Marcus_, Nov 08 2022
%Y Cf. A056545, A000354.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Aug 26 2004
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