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URL: https://oeis.org/A389988

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A389988
E.g.f. A(x) satisfies A(x) = exp(x * (1+x^3)^3 * A(x)).
2
1, 1, 3, 16, 197, 2376, 34087, 592264, 12222009, 287309584, 7572593771, 222023862864, 7174204979317, 253231860032776, 9693325191059343, 400025350334905096, 17706890216480517233, 836898448530271840416, 42067350910696875186259, 2240922577784674627963936
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-3*k),k)/(n-3*k)!.
E.g.f.: exp( -LambertW(-x*(1+x^3)^3) ).
MATHEMATICA
a[n_]:=n!*Sum[(n-3*k+1)^(n-3*k-1)*Binomial[3*(n-3*k), k]/(n-3*k)!, {k, 0, Floor[n/3]}]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, Oct 26 2025 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k+1)^(n-3*k-1)*binomial(3*(n-3*k), k)/(n-3*k)!);
(Magma) [Factorial(n) * &+[(n-3*k+1)^(n-3*k-1) * Binomial(3*(n-3*k), k) / Factorial(n-3*k) : k in [0..Floor(n/3)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 26 2025
CROSSREFS
Sequence in context: A174137 A385692 A166860 * A390185 A196562 A317073
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 21 2025
STATUS
approved