A384136 -id:A384136 - cp's OEIS frontend

A384137 a(n) = (4n)!/(3n)! * Sum_{k=1..n} 1/(3*n+k).

1, 15, 362, 12122, 520024, 27216936, 1681732464, 119823343440, 9671547654720, 872215286083200, 86920331742115200, 9485402065890543360, 1124985637517264409600, 144084905450972444851200, 19819350850103541715507200, 2914041773775561429169612800, 456069533875430113486232985600

Offset: 1

Seiichi Manyama, May 20 2025

nonn

Cf. A098118, A384136.

Cf. A382349.

a(n) = sum(k=0, n, k*(3*n+1)^(k-1)*abs(stirling(n, k, 1)));

a(n) = Sum_{k=0..n} k * (3*n+1)^(k-1) * |Stirling1(n,k)|.

a(n) = n! * [x^n] (-log(1 - x)/(1 - x)^(3*n+1)).

A384170 a(n) = 3^n * n! * binomial(5n/3,n) Sum_{k=1..n} 1/(2n+3k).

Original entry on oeis.org

1, 17, 423, 14198, 603194, 31069980, 1882538440, 131223122480, 10345975290000, 910393948446560, 88452245803947200, 9405081915991747200, 1086351888729412883200, 135456246872643979788800, 18134220756665496528460800, 2594357788916663689703168000, 395006034401484168868002560000

Offset: 1

Seiichi Manyama, May 21 2025

nonn

Cf. A384136.

a(n) = sum(k=0, n, k*(2*n+3)^(k-1)*3^(n-k)*abs(stirling(n, k, 1)));

a(n) = Sum_{k=0..n} k * (2*n+3)^(k-1) * 3^(n-k) * |Stirling1(n,k)|.

a(n) = n! * [x^n] ( -log(1 - 3*x)/(3 * (1 - 3*x)^(2*n/3+1)) ).

cp's OEIS Frontend

A384137 a(n) = (4n)!/(3n)! * Sum_{k=1..n} 1/(3*n+k).

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Formula

A384170 a(n) = 3^n * n! * binomial(5n/3,n) Sum_{k=1..n} 1/(2n+3k).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A384137 a(n) = (4*n)!/(3*n)! * Sum_{k=1..n} 1/(3*n+k).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A384170 a(n) = 3^n * n! * binomial(5*n/3,n) * Sum_{k=1..n} 1/(2*n+3*k).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A384137 a(n) = (4n)!/(3n)! * Sum_{k=1..n} 1/(3*n+k).

A384170 a(n) = 3^n * n! * binomial(5n/3,n) Sum_{k=1..n} 1/(2n+3k).