A030526 A convolution triangle of numbers obtained from A036070.

1, 10, 1, 80, 20, 1, 560, 260, 30, 1, 3584, 2720, 540, 40, 1, 21504, 24768, 7480, 920, 50, 1, 122880, 204288, 87552, 15840, 1400, 60, 1, 675840, 1562880, 908352, 225936, 28800, 1980, 70, 1, 3604480, 11264000, 8595200, 2813696, 483920, 47360, 2660, 80

Offset

1,2

Comments

a(n,m) := s1p(5; 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(5; n,m).

Links

Table of n, a(n) for n=1..44.

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

Formula

a(n, m) = 4*(4*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*(1-6*x+16*x^2-16*x^3)/(1-4*x)^4)^m.

Example

1;
10,1;
80,20,1;
560,260,30,1;
3584,2720,540,40,1;
...

Crossrefs

a(n, 1)= A036070(n-1). Row sums = A045624(n).

Sequence in context: A009209 A009227 A305996 * A327003 A206819 A178865

Adjacent sequences: A030523 A030524 A030525 * A030527 A030528 A030529

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved