A134279 -id:A134279 - cp's OEIS frontend

A134280 Triangle of numbers obtained from the partition array A134279.

1, 6, 1, 66, 6, 1, 1056, 102, 6, 1, 22176, 1452, 102, 6, 1, 576576, 32868, 1668, 102, 6, 1, 17873856, 779328, 35244, 1668, 102, 6, 1, 643458816, 23912064, 843480, 36540, 1668, 102, 6, 1, 26381811456, 812173824, 25416072, 857736, 36540, 1668, 102, 6, 1

Offset: 1

Wolfdieter Lang, Nov 13 2007

This triangle is named S2(6)'.

In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.

			[1]; [6,1]; [66,6,1]; [1056,102,6,1]; [22176,1452,102,6,1]; ...

W. Lang, First 10 rows and more.

Cf. A134275 (S2(5)').
Cf. A134281 (row sums).
Cf. A134282 (alternating row sums).

a(n,m)=sum(product(S2(6;j,1)^e(n,m,k,j),j=1..n),k=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,k,j) is the exponent of j in the k-th m part partition of n. S2(6;j,1) = A049385(n,1) = A008548(n) = (5*n-4)(!^5)(quintuple- or 5-factorials).

A134281 Row sums of triangle A134280 (S2(6)').

Original entry on oeis.org

1, 7, 73, 1165, 23737, 611221, 18690205, 668252677, 27220297405, 1246965912877, 63372307277821, 3539782399096237, 215467387904873101, 14196835617995678125, 1006540575704304853261, 76406049317127647613901

Offset: 1

Wolfdieter Lang, Nov 13 2007

Cf. A134282 (alternating row sums of triangle A134280).

a(n) = Sum_{m=1..n} A134280(n,m), n>=1.

a(n) = Sum_{k=1..p(n)} A134279(n,k), with p(n) = A000041(n) (number of partitions of n).

cp's OEIS Frontend

A134280 Triangle of numbers obtained from the partition array A134279.

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