A350366 -id:A350366 - cp's OEIS frontend

A384088 a(n) = [x^n] Product_{k=1..n} ((1 + kx)/(1 - kx))^4.

1, 8, 288, 18528, 1728000, 211687080, 32159822688, 5835397918336, 1231573968949248, 296447550279133320, 80158746419240852000, 24057027574081163030688, 7935414295799696292767232, 2853706409310576479751168168, 1111199574070700473937862463200, 465782420445680979210397280524800

Offset: 0

Vaclav Kotesovec, May 19 2025

nonn

Cf. A384031, A384060.

Cf. A350366, A384086, A384087, A351764.

Table[SeriesCoefficient[Product[(1+k*x)^4/(1-k*x)^4, {k, 1, n}], {x, 0, n}], {n, 0, 16}]

a(n) ~ c * d^n * n! / n, where d = 29.85915450232266280267400661836716424701025678171993103713550551... and c = 0.415660498916272367812330643610916948922178337726778287649763513...

A383839 a(n) = [x^n] 1/(1 - nx) Product_{k=0..n-1} (1 + kx)/(1 - kx).

Original entry on oeis.org

1, 1, 10, 177, 4576, 156145, 6627006, 336562177, 19906794496, 1344082891761, 102012257669950, 8597688151223281, 796733925564191616, 80516951813773009249, 8812696026991760928766, 1038540275078155878285825, 131107274213106172807069696, 17652158052761888943436783009

Offset: 0

Seiichi Manyama, May 14 2025

nonn

Cf. A350366, A383767.

a(n) = sum(k=0, n, abs(stirling(n, k, 1))*stirling(k+n, n, 2));

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * Stirling2(k+n,n).

cp's OEIS Frontend

A384088 a(n) = [x^n] Product_{k=1..n} ((1 + kx)/(1 - kx))^4.

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Mathematica

Formula

A383839 a(n) = [x^n] 1/(1 - nx) Product_{k=0..n-1} (1 + kx)/(1 - kx).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A384088 a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^4.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A383839 a(n) = [x^n] 1/(1 - n*x) * Product_{k=0..n-1} (1 + k*x)/(1 - k*x).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A384088 a(n) = [x^n] Product_{k=1..n} ((1 + kx)/(1 - kx))^4.

A383839 a(n) = [x^n] 1/(1 - nx) Product_{k=0..n-1} (1 + kx)/(1 - kx).