A390094 E.g.f. A(x) satisfies A(x) = exp( x * (1-x^2)^2 * A(x)^2 ).

1, 1, 5, 37, 489, 8881, 207133, 5858805, 194718737, 7434889921, 320735744181, 15428975581669, 818940719873785, 47545398370803633, 2997307286307363149, 203902192640016611701, 14888734670837177420577, 1161500796952432440824065, 96412935099709440162282853

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

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

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

Mathematica

Table[n!*Sum[(-1)^k*(2*(n-2*k)+1)^(n-2*k-1)*Binomial[2*(n-2*k), k]/(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 04 2025 *)

Prog

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

Crossrefs

Cf. A390060.

Sequence in context: A003709 A361281 A286928 * A390270 A321042 A244820

Adjacent sequences: A390091 A390092 A390093 * A390095 A390096 A390097

Keyword

nonn

Author

Seiichi Manyama, Oct 23 2025

Status

approved