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URL: https://oeis.org/A390185

⇱ A390185 - OEIS

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A390185
E.g.f. A(x) satisfies A(x) = exp( x/(1-x^3)^3 * A(x) ).
2
1, 1, 3, 16, 197, 2376, 34087, 607384, 12584889, 296018704, 7832052971, 230645891664, 7478933822197, 264797098197256, 10167880686233103, 420931959309356296, 18689915386448958833, 886051401327505565856, 44672857610031084052819, 2386887927401707441700896
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)^(n-3*k-1) * binomial(3*n-8*k-1,k)/(n-3*k)!.
E.g.f.: exp( -LambertW(-x/(1-x^3)^3) ).
MATHEMATICA
Table[n!*Sum[(n-3*k+1)^(n-3*k-1)*Binomial[3*n-8*k-1, k]/(n-3*k)!, {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 04 2025 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k+1)^(n-3*k-1)*binomial(3*n-8*k-1, k)/(n-3*k)!);
(Magma) [Factorial(n) * &+[(n-3*k+1)^(n-3*k-1)* Binomial(3*n-8*k-1, k) / Factorial(n-3*k) : k in [0..Floor(n/3)]] : n in [0..25] ]; // Vincenzo Librandi, Nov 04 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 28 2025
STATUS
approved