A378094 E.g.f. satisfies A(x) = exp( x^2 * A(x) / (1-x) ) / (1-x).

1, 1, 4, 24, 204, 2220, 29640, 469560, 8623440, 180306000, 4231815840, 110217270240, 3155551439040, 98529432281280, 3332752472649600, 121416875166787200, 4740431035737196800, 197475789694088505600, 8743499113411321459200, 410050296758706725721600

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: exp( -LambertW(-x^2/(1-x)^2) )/(1-x).

a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(n,2*k)/k!.

a(n) ~ sqrt(2) * (1 + exp(1/2))^(n + 3/2) * n^(n-1) / exp(n - 1/4). - Vaclav Kotesovec, Nov 16 2024

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(n, 2*k)/k!);

Crossrefs

Cf. A352410, A378095.

Cf. A371038.

Sequence in context: A089946 A343094 A012244 * A342168 A240429 A240297

Adjacent sequences: A378091 A378092 A378093 * A378095 A378096 A378097

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2024

Status

approved