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

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.

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

Wolfdieter 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

Triangle begins:
  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;
Flatten[Table[a[n, m], {n, 1, 8}, {m, 1, n}]][[1 ;; 36]]
(* Jean-François Alcover, Jun 17 2011 *)

Crossrefs

Cf. A132058 (row sums), A132059 (negative of alternating row sums).

Sequence in context: A040810 A040811 A051000 * A363590 A292919 A040777

Adjacent sequences: A132054 A132055 A132056 * A132058 A132059 A132060

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Sep 14 2007

Status

approved