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URL: https://oeis.org/A389786

⇱ A389786 - OEIS

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A389786
E.g.f. A(x) satisfies A(x) = exp(x^2 * (1+x)^3 * A(x)).
2
1, 0, 2, 18, 108, 1200, 18120, 272160, 4987920, 107231040, 2511311040, 65616566400, 1896591533760, 59500273472640, 2022710729719680, 74145485378764800, 2910426333592377600, 121883776482717849600, 5425975658285467084800, 255811158734931659059200
OFFSET
0,3
LINKS
FORMULA
E.g.f.: exp( -LambertW(-x^2 * (1+x)^3) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(3*k,n-2*k)/k!.
MATHEMATICA
Table[n!*Sum[(k+1)^(k-1)*Binomial[3*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, (k+1)^(k-1)*binomial(3*k, n-2*k)/k!);
CROSSREFS
Cf. A387993.
Sequence in context: A112328 A370732 A389818 * A038721 A308700 A064837
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 14 2025
STATUS
approved