A390647 E.g.f. A(x) satisfies A(x) = 1 + x^2*exp(x)*A(x)^3.

1, 0, 2, 6, 84, 740, 12990, 201642, 4475576, 99719496, 2735268570, 78877307630, 2605450510212, 91724294787996, 3563867498039030, 147715968506783250, 6618151929336030960, 315162521018238297872, 16017517201006303914546, 861049460872319850568278

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)} k^(n-2*k) * A001764(k)/(n-2*k)!.

Mathematica

Join[{1}, Table[Factorial[n]*Sum[k^(n-2*k)*Binomial[3*k, k]/((2*k+1)*Factorial[n-2*k]), {k, 0, Floor[n/2]}], {n, 1, 20}]] (* Vincenzo Librandi, Dec 27 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(3*k, k)/((2*k+1)*(n-2*k)!));
(Magma) [Factorial(n)*&+[k^(n-2*k)*Binomial(3*k, k)/((2*k+1)*Factorial((n-2*k))): k in [0..Floor(n/2)]] : n in [0..30] ]; // Vincenzo Librandi, Dec 27 2025

Crossrefs

Cf. A358080, A390646.

Cf. A001764.

Sequence in context: A325949 A055706 A376494 * A376474 A370984 A118537

Adjacent sequences: A390644 A390645 A390646 * A390648 A390649 A390650

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 13 2025

Status

approved