A092086 -id:A092086 - cp's OEIS frontend

A092083 A convolution triangle of numbers obtained from A034789.

1, 21, 1, 546, 42, 1, 15561, 1533, 63, 1, 466830, 54054, 2961, 84, 1, 14471730, 1885338, 124740, 4830, 105, 1, 458960580, 65542932, 4977882, 236880, 7140, 126, 1, 14801478705, 2277656901, 192582117, 10661301, 399735, 9891, 147, 1

Offset: 1

Wolfdieter Lang, Mar 19 2004

a(n,1) = A034789(n). a(n,m)=: s2(7; n,m), a member of a sequence of unsigned triangles including s2(2; n,m)=A007318(n-1,m-1) (Pascal's triangle). s2(3; n,m)= A035324(n,m), s2(4; n,m)= A035529(n,m), s2(5; n,m)= A048882(n,m), s2(6; n,m)= A049375.

			{1}; {21,1}; {546,42,1}; {15561,1533,63,1}; ...

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
W. Lang, First 10 rows.

Cf. A092086 (row sums), A092087 (alternating row sums).

a(n, m) = 6*(6*(n-1)+m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n

A132058 Row sums of triangle A132057 (s2(8)).

Original entry on oeis.org

1, 29, 1037, 40559, 1667583, 70782699, 3071608779, 135473190854, 6049729693582, 272822775416318, 12401578633961126, 567447248339504450, 26107796156861857866, 1206858263561650517658, 56014709781906608746434

Offset: 1

Wolfdieter Lang Sep 14 2007

Cf. A092086 (row sums of s2(7)=A092083).

a(n)=sum(A132057(n, m), m=1..n), n>=1.

G.f.: (-1 + (1-49*x)^(-1/7))/(8-(1-49*x)^(-1/7)).

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cp's OEIS Frontend

A092083 A convolution triangle of numbers obtained from A034789.

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