A132057 - OEIS

A132057

A convolution triangle of numbers obtained from A034904.

1, 28, 1, 980, 56, 1, 37730, 2744, 84, 1, 1531838, 130340, 5292, 112, 1, 64337196, 6136956, 299782, 8624, 140, 1, 2766499428, 288408120, 16120314, 568008, 12740, 168, 1, 121034349975, 13561837212, 841627332, 34401528, 956970, 17640, 196, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(n,1) = A034904(n). a(n,m)=: s2(8; 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; s2(7; n,m)=A092083.

LINKS

Table of n, a(n) for n=1..36.

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

W. Lang, First 10 rows.

FORMULA

a(n, m) = 7*(7*(n-1)+m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1.

G.f. for m-th column: ((-1+(1-49*x)^(-1/7))/7)^m.

EXAMPLE

{1}; {28,1}; {980,56,1}; (37730,2744,84,1);...

MATHEMATICA

a[n_, m_] := a[n, m] = 7*(7*(n-1) + m)*a[n-1, m]/n + m*a[n-1, m-1]/n;

a[n_, m_] /; n < m = 0; a[_, 0] = 0; a[1, 1] = 1;