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A376517
E.g.f. satisfies A(x) = exp(x^2 * (1 + x) * A(x)).
1
1, 0, 2, 6, 36, 360, 3000, 40320, 532560, 8527680, 152591040, 2987107200, 65408333760, 1544664401280, 39767121313920, 1100734899264000, 32661264290054400, 1034874195222067200, 34834463447361177600, 1242657968679512985600, 46804841790705090892800
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp( -LambertW(-x^2 * (1+x)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(k,n-2*k)/k!.
a(n) ~ sqrt((2 + 3*r)/(1 + r)) * n^(n-1) / (exp(n-1) * r^n), where r = (-1 + 2*cosh(log(-1 + (3*(9 + sqrt(81 - 12*exp(1))))/(2*exp(1)))/3))/3. - Vaclav Kotesovec, Sep 26 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^2*(1+x)))))
(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(k, n-2*k)/k!);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 26 2024
STATUS
approved