A380425 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * exp(x * A(x)^(1/2)) ).

1, 2, 12, 116, 1592, 28472, 630028, 16649348, 512197456, 17993496176, 711065689364, 31231930472492, 1509776777566648, 79670350504209896, 4557716010219325468, 280992142281969312548, 18574365176584473753248, 1310583528463442480750048, 98318677221689347734929956

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..360

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A162695.

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

Prog

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

Crossrefs

Cf. A162695, A380426, A380427.

Cf. A360474, A380406.

Sequence in context: A214222 A227459 A377716 * A372200 A290840 A012628

Adjacent sequences: A380420 A380422 A380423 * A380426 A380427 A380430

Keyword

nonn,new

Author

Seiichi Manyama, Jan 24 2025

Status

approved