A185412 Triangle T(n,m) read by rows: the matrix product A130595 * A156919.

1, 1, 1, 1, 8, 1, 1, 33, 33, 1, 1, 112, 378, 112, 1, 1, 353, 2938, 2938, 353, 1, 1, 1080, 18987, 44912, 18987, 1080, 1, 1, 3265, 111051, 520523, 520523, 111051, 3265, 1, 1, 9824, 612820, 5131040, 9998182, 5131040, 612820, 9824, 1

Offset: 0

Author

Paul Barry, Jan 26 2011

Keywords

• nonn
• easy
• tabl

Comments

Row sums are A165968(n+1).

Because A130595 is the inverse of the Pascal triangle A007318, we have A007318 *(this lower triangular matrix) = A156919.

Examples

			Triangle begins in row n=0 with columns 0 <= m <= n:
  1;
  1,    1;
  1,    8,      1;
  1,   33,     33,       1;
  1,  112,    378,     112,       1;
  1,  353,   2938,    2938,     353,       1;
  1, 1080,  18987,   44912,   18987,    1080,      1;
  1, 3265, 111051,  520523,  520523,  111051,   3265,    1;
  1, 9824, 612820, 5131040, 9998182, 5131040, 612820, 9824, 1;
		

Programs

Maple

A156919 := proc(n,m) if n=m then 1; elif m=0 then 2^n ; elif m<0 or m>n then 0; else 2*(m+1)*procname(n-1,m)+(2*n-2*m+1)*procname(n-1,m-1) ; end if; end proc:
A130595 := proc(n,m) (-1)^(n+m)*binomial(n,m) ; end proc:
A185412 := proc(n,m) local a,j; a := 0 ; for j from m to n do a := a+A130595(n,j)*A156919(j,m) ; end do: a ; end proc: # R. J. Mathar, Feb 03 2011

Formula

G.f.: 1/(1+x-xy-2x/(1-3xy/(1+x-4x/(1-5xy/(1+x-6x/(1-7xy/(1+x-8x/(1-9xy/(1+ ... (continued fraction).