A382985 Coefficient of x^4 in expansion of (x+1) * (x+4) * ... * (x+3*n-2).

0, 0, 0, 0, 1, 35, 1005, 28700, 859369, 27458613, 941164860, 34617398640, 1364003226036, 57425577775852, 2575788307560104, 122732603903789880, 6194752323883374224, 330320189407442698000, 18560921582024101872576, 1096473082032417593216832

Offset

0,6

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=4..n} 3^(n-k) * binomial(k,4) * |Stirling1(n,k)|.

E.g.f.: f(x) * log(f(x))^4 / 24, where f(x) = 1/(1 - 3*x)^(1/3).

Prog

(PARI) a(n) = polcoef(prod(k=0, n-1, x+3*k+1), 4);

Crossrefs

Column k=4 of A286718.

Cf. A028341.

Sequence in context: A002453 A240826 A210313 * A049395 A278723 A215296

Adjacent sequences: A382982 A382983 A382984 * A382986 A382987 A382988

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2025

Status

approved