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A375633
Expansion of e.g.f. exp(x^2) / (1 - x * exp(x^2/2)).
3
1, 1, 4, 15, 84, 555, 4440, 41265, 438480, 5240025, 69582240, 1016350335, 16194911040, 279560396115, 5197054262400, 103514720133825, 2199255573715200, 49645309340451825, 1186599954328588800, 29937224154635772975, 795051251297099596800
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} ((n-2*k+2)/2)^k/k!.
MAPLE
A375633 := proc(n)
n!*add(((n-2*k+2)/2)^k/k!, k=0..floor(n/2)) ;
end proc:
seq(A375633(n), n=0..60) ; # R. J. Mathar, Aug 23 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2)/(1-x*exp(x^2/2))))
(PARI) a(n) = n!*sum(k=0, n\2, ((n-2*k+2)/2)^k/k!);
CROSSREFS
Sequence in context: A151379 A130679 A243048 * A107874 A237627 A034496
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 22 2024
STATUS
approved