A375629 Expansion of e.g.f. exp(2*x) / (1 - x^2 * exp(x)).
1, 2, 6, 26, 148, 1052, 8974, 89294, 1015480, 12991832, 184682554, 2887850858, 49261993444, 910356170804, 18117379906630, 386315966673638, 8786555389140976, 212335975835710256, 5433155029435593970, 146744457899073450050, 4172032796528725318876
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^2*exp(x)))) -
PARI
a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(n-2*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (k+2)^(n-2*k)/(n-2*k)!.