A387974 E.g.f. A(x) satisfies A(x) = exp( x^2*A(x)^2 ) * (1+x*A(x)).

1, 1, 4, 30, 324, 4680, 84720, 1846320, 47108880, 1378097280, 45484165440, 1672298369280, 67787887970880, 3003743936793600, 144452748779539200, 7493456461217126400, 417100158353348870400, 24797329866957724876800, 1568278221284077765862400

Offset

0,3

Links

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

Formula

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

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

Mathematica

Table[n!*Sum[(n+1)^(k-1)*Binomial[n+1, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Oct 27 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(k-1)*binomial(n+1, n-2*k)/k!);
(Magma) [Factorial(n) * &+[(n+1)^(k-1)* Binomial(n+1, n-2*k) / Factorial(k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 27 2025

Crossrefs

Cf. A387971, A387972, A387973.

Cf. A088690.

Sequence in context: A211828 A277759 A392786 * A006149 A207833 A121413

Adjacent sequences: A387971 A387972 A387973 * A387975 A387976 A387977

Keyword

nonn

Author

Seiichi Manyama, Oct 12 2025

Status

approved