A360474 E.g.f. satisfies A(x) = exp( x * A(x)^2 * exp(x * A(x)^2) ).

1, 1, 7, 94, 1921, 53036, 1849789, 78070462, 3869909537, 220427550712, 14188370562901, 1018570771664546, 80692202644742737, 6992855583524143204, 658076908751441373965, 66833181471569822199886, 7285736943975575120653249, 848589321771735983890457072

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

a(n) ~ 2^(n - 1/2) * n^(n-1) * s^(2*n + 1) * log(s)^(n + 1/2) / (sqrt(1 + 2*log(s) - 4*log(s)^2) * exp(n) * (1 - 2*log(s))^n), where s = 1.473428520956658037187728756446912746332041803082... is the root of the equation 2*log(s)*(1 + LambertW(log(s))) = 1. - Vaclav Kotesovec, Feb 17 2023

Mathematica

Join[{1}, Table[Sum[k^(n-k) * (2*n+1)^(k-1) * Binomial[n, k], {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Feb 17 2023 *)

Prog

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

Crossrefs

Cf. A162695, A360473.

Sequence in context: A221384 A243679 A367162 * A327843 A015225 A183521

Adjacent sequences: A360471 A360472 A360473 * A360475 A360476 A360477

Keyword

nonn

Author

Seiichi Manyama, Feb 08 2023

Status

approved