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URL: https://oeis.org/A389787

⇱ A389787 - OEIS

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A389787
E.g.f. A(x) satisfies A(x) = exp(x^3 * (1+x)^2 * A(x)).
2
1, 0, 0, 6, 48, 120, 1080, 30240, 362880, 3144960, 63504000, 1596672000, 28041552000, 508540032000, 14108353459200, 399015038822400, 9887761787904000, 276606256582656000, 9380606786475724800, 315034453620452966400, 10382287674793402368000, 380907748942210473984000
OFFSET
0,4
LINKS
FORMULA
E.g.f.: exp( -LambertW(-x^3 * (1+x)^2) ).
a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(2*k,n-3*k)/k!.
MATHEMATICA
terms = 22; A[_] = 0; Do[A[x_] = Exp[x^3*(1+x)^2* A[x]] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]*Range[0, terms-1]! (* Stefano Spezia, Oct 17 2025 *)
Table[n!*Sum[(k+1)^(k-1)*Binomial[2*k, n-3*k]/k!, {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 05 2025 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(2*k, n-3*k)/k!);
CROSSREFS
Cf. A387994.
Sequence in context: A341683 A259121 A389820 * A052651 A387994 A153796
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 14 2025
STATUS
approved