A396509 a(n) = 2 * (4*n+2)^(n-1).

1, 2, 20, 392, 11664, 468512, 23762752, 1458000000, 105046700288, 8695584276992, 813342767698944, 84841494965553152, 9765625000000000000, 1229575252353016799232, 168110140833113738264576, 24803538869315053824278528, 3928158732213644200735997952, 664658611392020000000000000000

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..300

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

Formula

E.g.f.: exp(-1/2 * LambertW(-4*x)).

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052774.

E.g.f. A(x) satisfies:

(1) A(x) = exp(2*x*A(x)^2).

(2) A(x) = 1/A(-x*A(x)^4).

Mathematica

A396509[n_] := 2*(4*n + 2)^(n - 1); Array[A396509, 20, 0] (* Paolo Xausa, May 28 2026 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-1/2*lambertw(-4*x))))

Crossrefs

Column k=1 of A396504.

Cf. A052774, A385085.

Sequence in context: A376391 A376394 A218306 * A009236 A078698 A090728

Adjacent sequences: A396506 A396507 A396508 * A396510 A396511 A396512

Keyword

nonn,easy

Author

Seiichi Manyama, May 28 2026

Status

approved