A384030 -id:A384030 - cp's OEIS frontend

A384029 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^4.

1, 0, 6, 180, 7206, 370880, 23477380, 1768061064, 154544373158, 15387101825184, 1719596420272980, 213181689525888600, 29036623040055512332, 4310582688852993653568, 692756995680614782818992, 119830419866883597939018000, 22198322332579642585088580870, 4384714751330840129324051474880

Offset: 0

Seiichi Manyama, May 17 2025

nonn

Cf. A342111, A384018.
Cf. A384027, A384030.
Cf. A384031.

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

a(n) = Sum_{0<=i, j, k, l<=n and i+j+k+l=3*n} |Stirling1(n,i) * Stirling1(n,j) * Stirling1(n,k) * Stirling1(n,l)|.

A384027 a(n) = [x^(3n)] Product_{k=0..n-1} (1 + kx)^4.

Original entry on oeis.org

1, 0, 0, 0, 1296, 2764800, 8041766400, 34726710251520, 219045033712578816, 1956771788423009992704, 24009126017002632247173120, 393692515265172002272138690560, 8424620140673205407840209386541056, 230472036551670538296109810120063451136, 7917891968134805796965854747528387122954240

Offset: 0

Seiichi Manyama, May 17 2025

nonn

Cf. A342111, A384026.

Cf. A384029, A384030.

a(n) = sum(i=0, n, sum(j=0, n-i, sum(k=0, n-i-j, abs(stirling(n, i, 1)*stirling(n, j, 1)*stirling(n, k, 1)*stirling(n, n-i-j-k, 1)))));

a(n) = Sum_{i, j, k, l>=0 and i+j+k+l=n} |Stirling1(n,i) * Stirling1(n,j) * Stirling1(n,k) * Stirling1(n,l)|.

cp's OEIS Frontend

A384029 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^4.

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Formula

A384027 a(n) = [x^(3n)] Product_{k=0..n-1} (1 + kx)^4.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A384029 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^4.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A384027 a(n) = [x^(3*n)] Product_{k=0..n-1} (1 + k*x)^4.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A384027 a(n) = [x^(3n)] Product_{k=0..n-1} (1 + kx)^4.