A373741 Expansion of e.g.f. exp(x^2/2 * (1 + x)^3).

1, 0, 1, 9, 39, 150, 1365, 13545, 105945, 918540, 10603845, 127806525, 1468823895, 18253765530, 257397445305, 3770163121725, 55637459903025, 866703333295800, 14468243658093225, 250223925107581425, 4426399346291497575, 81488489549760042750

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*k,n-2*k)/(2^k * k!).

a(n) = (n-1)/2 * (2*a(n-2) + 9*(n-2)*a(n-3) + 12*(n-2)*(n-3)*a(n-4) + 5*(n-2)*(n-3)*(n-4)*a(n-5)).

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x^2/2 (1+x)^3], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 26 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, binomial(3*k, n-2*k)/(2^k*k!));

Crossrefs

Cf. A361567, A373740.

Cf. A116090.

Sequence in context: A212143 A294845 A124851 * A317019 A124041 A264085

Adjacent sequences: A373738 A373739 A373740 * A373742 A373743 A373744

Keyword

nonn

Author

Seiichi Manyama, Jun 16 2024

Status

approved