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A358264
Expansion of e.g.f. 1/(1 - x * exp(x^2/2)).
2
1, 1, 2, 9, 48, 315, 2520, 23415, 248640, 2972025, 39463200, 576413145, 9184855680, 158550787395, 2947473809280, 58707685211175, 1247293022976000, 28156003910859825, 672972205556851200, 16978695795089253225, 450907982644863744000, 12573634144960773960075
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * k!).
a(n) ~ n! / ((1 + LambertW(1)) * LambertW(1)^(n/2)). - Vaclav Kotesovec, Nov 13 2022
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^2/2))))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 06 2022
STATUS
approved