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A389986

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

1, 1, 3, 34, 341, 4536, 78007, 1567504, 36794025, 989152768, 29889022571, 1004478465024, 37175642202877, 1502417449013248, 65848171170656799, 3111213459528196096, 157653357237027706193, 8529212883879336738816, 490709473157067629402323

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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)} (n-2*k+1)^(n-2*k-1) * binomial(3*(n-2*k),k)/(n-2*k)!.

E.g.f.: exp( -LambertW(-x*(1+x^2)^3) ).

MATHEMATICA

a[n_]:=n!*Sum[(n-2*k+1)^(n-2*k-1)*Binomial[3*(n-2*k), k]/(n-2*k)!, {k, 0, Floor[n/2]}]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, Oct 26 2025 *)

PROG

(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)^(n-2*k-1)*binomial(3*(n-2*k), k)/(n-2*k)!);

(Magma) [Factorial(n) * &+[(n-2*k+1)^(n-2*k-1) * Binomial(3*(n-2*k), k) / Factorial(n-2*k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 26 2025

CROSSREFS

Cf. A376577, A387013.

Cf. A376145, A389988.

Sequence in context: A246384 A066265 A268802 * A390183 A284891 A231593

Adjacent sequences: A389983 A389984 A389985 * A389987 A389988 A389989

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 21 2025

STATUS

approved

URL: https://oeis.org/A389986

⇱ A389986 - OEIS