A092087 -id:A092087 - 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

A132059 Alternating row sums of triangle A132057 (s2(8)).

Original entry on oeis.org

1, 27, 925, 35069, 1406679, 58491537, 2493656187, 108280678092, 4768395658314, 212335592489544, 9540877059969102, 431908789303835976, 19675192863275361294, 901089855844979674068, 41459199062515242868098

Offset: 1

Wolfdieter Lang Sep 11 2007

Cf. A092087 (alternating row sums of s2(7)=A092083).

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

G.f.: (-1 +(1-49*x)^(-1/7))/(6+(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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