A375172 Expansion of e.g.f. exp( x^2/(1-x)^3 ) / (1-x).
1, 1, 4, 30, 276, 2940, 36120, 507360, 8032080, 141235920, 2725107840, 57151211040, 1293129351360, 31376876731200, 812303844992640, 22338850742208000, 650081402588217600, 19951131574037664000, 643805564147435289600, 21785365857810973017600
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/(1-x)^3)/(1-x))) -
PARI
a(n) = n!*sum(k=0, n\2, binomial(n+k, n-2*k)/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n+k,n-2*k)/k!.