A384026 -id:A384026 - cp's OEIS frontend

A384018 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^3.

1, 0, 3, 63, 1767, 63690, 2822740, 148810032, 9104502015, 634448680884, 49622704133175, 4305280182748875, 410376649359397380, 42633179822414174760, 4794685285831034253660, 580373328155358031572600, 75234419898396217903091151, 10398952352945773993329785448, 1526704288048697734221906020641

Offset: 0

Seiichi Manyama, May 17 2025

nonn

Cf. A342111, A384029.

Cf. A384026.

a(n) = sum(i=0, n, sum(j=0, 2*n-i, abs(stirling(n, i, 1)*stirling(n, j, 1)*stirling(n, 2*n-i-j, 1))));

a(n) = Sum_{0<=i, j, k<=n and i+j+k=2*n} |Stirling1(n,i) * Stirling1(n,j) * Stirling1(n,k)|.

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

A384018 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^3.

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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

A384018 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^3.

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.