A171589 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A104455.

1, 4, 1, 17, 8, 1, 77, 50, 12, 1, 371, 290, 99, 16, 1, 1890, 1647, 703, 164, 20, 1, 10095, 9366, 4644, 1380, 245, 24, 1, 56040, 53853, 29592, 10434, 2385, 342, 28, 1, 320795, 314234, 185411, 74084, 20345, 3782, 455, 32, 1

Offset: 0

Author

Philippe Deléham, Dec 12 2009

Keywords

• nonn
• tabl

Comments

Equal to B*A171568 = A125906*B^(-1), B = A007318.

Examples

			Triangle begins :
1
4, 1
17, 8, 1
77, 50, 12, 1
371, 290, 99, 16, 1
1890, 1647, 703, 164, 20, 1
10095, 9366, 4644, 1380, 245, 24, 1
Production matrix begins
4, 1
1, 4, 1
1, 1, 4, 1
1, 1, 1, 4, 1
1, 1, 1, 1, 4, 1
1, 1, 1, 1, 1, 4, 1
1, 1, 1, 1, 1, 1, 4, 1
1, 1, 1, 1, 1, 1, 1, 4, 1
... - _Philippe Deléham_, Mar 05 2013
		

Crossrefs

Cf. A104455, A125906, A171568,

Formula

T(n,0)-T(n,1)=3^n.

T(n,k) = T(n-1,k-1) + 4*T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i). - Philippe Deléham, Feb 23 2012