A030527 A convolution triangle of numbers obtained from A036083.

1, 15, 1, 175, 30, 1, 1750, 575, 45, 1, 15750, 8750, 1200, 60, 1, 131250, 114625, 24375, 2050, 75, 1, 1031250, 1347500, 414750, 52000, 3125, 90, 1, 7734375, 14575000, 6208125, 1084875, 95000, 4425, 105, 1, 55859375, 147468750, 84184375

Offset

1,2

Comments

a(n,m) := s1p(6; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle). Signed version: (-1)^(n-m)*a(n,m) := s1(6; n,m).

Links

Table of n, a(n) for n=1..39.

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

Formula

a(n, m) = 5*(5*m+n-1)*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: (x*(1-10*x+50*x^2-125*x^3+125*x^4)/(1-5*x)^5)^m.

Example

Triangle begins:
  {1};
  {15,1};
  {175,30,1};
  {1750,575,45,1};
  {15750,8750,1200,60,1};
  ...

Crossrefs

a(n, 1) = A036083(n-1). Row sums = A046088(n).

Sequence in context: A126141 A131514 A049327 * A027467 A049375 A049224

Adjacent sequences: A030524 A030525 A030526 * A030528 A030529 A030530

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved