A387964 E.g.f. A(x) satisfies A(x) = exp( x^2*A(x)^2 / (1-x*A(x)) ) / (1-x*A(x)).

1, 1, 6, 60, 900, 18000, 451920, 13675200, 484762320, 19710432000, 904491735840, 46247508679680, 2607566629187520, 160737221662617600, 10754709223658400000, 776272412214422323200, 60126250923876884947200, 4974480172611199195545600, 437832291517037950038105600

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..350

Formula

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

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

Mathematica

Table[n!*Sum[(n+1)^(k-1)*Binomial[2*n-k, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 06 2025 *)

Prog

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

Crossrefs

Cf. A387965, A387966.

Cf. A144085.

Sequence in context: A010040 A138379 A064815 * A331120 A368505 A296956

Adjacent sequences: A387961 A387962 A387963 * A387965 A387966 A387967

Keyword

nonn

Author

Seiichi Manyama, Oct 12 2025

Status

approved