A371063 E.g.f. satisfies A(x) = 1 + x^2/2*exp(x*A(x)).
1, 0, 1, 3, 6, 40, 375, 2541, 21028, 264636, 3303765, 41219695, 625493946, 10676900598, 185753808331, 3495429297465, 72963017028840, 1606964677740376, 37107535997019753, 918150959889615771, 24110308315512081550, 662150320109499176130, 19105058680403510485671
Offset: 0
Keywords
Programs
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Mathematica
nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^3/2]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *) -
PARI
a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(n-2*k+1, k)/(2^k*(n-2*k+1)*(n-2*k)!));
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k) * binomial(n-2*k+1,k)/( 2^k*(n-2*k+1)*(n-2*k)! ).