A171505 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A059738.

1, 3, 1, 10, 6, 1, 34, 29, 9, 1, 117, 128, 57, 12, 1, 405, 538, 309, 94, 15, 1, 1407, 2192, 1533, 604, 140, 18, 1, 4899, 8740, 7179, 3453, 1040, 195, 21, 1, 17083, 34296, 32278, 18264, 6730, 1644, 259, 24, 1, 59629, 132929, 140790, 91372, 39668, 11877, 2443

Offset: 0

Author

Philippe Deléham, Dec 10 2009

Keywords

• nonn
• tabl

Comments

Equal to B*A096164 = A171488*B, B=A007318.

Examples

			Triangle begins :
1 ;
3, 1 ;
10, 6, 1 ;
34, 29, 9, 1 ;
117, 128, 57, 12, 1 ; ...
		

Crossrefs

Cf. A097609, A064189, A171488, A096164

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A005043(n), A001006(n), A005773(n+1), A059738(n) for x = -3, -2, -1, 0 respectively.

T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*(-2)^i. - Philippe Deléham, Feb 23 2012