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A362524
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) / (2^k * k! * (n-2*k)!).
1
1, 1, 2, 4, 16, 56, 391, 2017, 20504, 139456, 1867681, 15751451, 262263442, 2638794094, 52589415971, 614628436801, 14274125637256, 190012483804952, 5041005195499849, 75288391385094811, 2246914521052963166, 37204717212894726706, 1233884675800841217847
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x - LambertW(-x^2/2)) = -2 * LambertW(-x^2/2)/x^2 * exp(x).
MATHEMATICA
Table[n!Sum[(k+1)^(k-1)/(2^k k!(n-2k)!), {k, 0, Floor[n/2]}], {n, 0, 25}] (* Harvey P. Dale, Mar 30 2024 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^2/2))))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 23 2023
STATUS
approved