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URL: https://oeis.org/A390182

⇱ A390182 - OEIS

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A390182
E.g.f. A(x) satisfies A(x) = exp( x/(1-x^2)^2 * A(x) ).
2
1, 1, 3, 28, 269, 3576, 57607, 1108864, 24846873, 635796352, 18311102891, 586410177024, 20678425176037, 796318634865664, 33257372618180271, 1497378036098031616, 72306399781070950193, 3727918866731406360576, 204398098382050669814995, 11876234811106617124323328
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(n-2*k-1) * binomial(2*n-3*k-1,k)/(n-2*k)!.
E.g.f.: exp( -LambertW(-x/(1-x^2)^2) ).
MATHEMATICA
Table[n!*Sum[(n-2*k+1)^(n-2*k-1)*Binomial[2*n-3*k-1, k]/(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 03 2025 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)^(n-2*k-1)*binomial(2*n-3*k-1, k)/(n-2*k)!);
(Magma) [Factorial(n) * &+[(n-2*k+1)^(n-2*k-1)* Binomial(2*n-3*k-1, k) / Factorial(n-2*k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Nov 03 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 28 2025
STATUS
approved