A114188 Riordan array (1/(1-x),x(1+x)/(1-x)^2).

1, 1, 1, 1, 4, 1, 1, 9, 7, 1, 1, 16, 26, 10, 1, 1, 25, 70, 52, 13, 1, 1, 36, 155, 190, 87, 16, 1, 1, 49, 301, 553, 403, 131, 19, 1, 1, 64, 532, 1372, 1462, 736, 184, 22, 1, 1, 81, 876, 3024, 4446, 3206, 1216, 246, 25, 1, 1, 100, 1365, 6084, 11826, 11584, 6190, 1870, 317

Offset: 0

Author

Paul Barry, Nov 16 2005

Keywords

• easy
• nonn
• tabl

Comments

Product of A007318 and A113953, that is, (1/(1-x),x/(1-x))*(1,x(1+2x)).

Row sums are A025192. Diagonal sums are A052980.

Inverse is A114189. A signed version is A110511.

Examples

			Triangle begins
1;
1, 1;
1, 4, 1;
1, 9, 7, 1;
1, 16, 26, 10, 1;
1, 25, 70, 52, 13, 1;
1, 36,155,190, 87, 16, 1;
		

Links

• P. Barry, A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.5.4.

Crossrefs

Cf. A007318, A025192, A052980, A110511, A113953, A114189.

Formula

T(n, k) = Sum_{j=0..n} C(n, j)*C(k, j-k)2^(j-k).

T(n, k) = Sum_{j=0..n-k} C(k, j)*C(n+k-j, 2k).

T(n,k) = 2*T(n-1,k)+T(n-1,k-1)-T(n-2,k)+T(n-2,k-1), T(0,0)=T(1,0)=T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 11 2014

G.f.: 1/(1-y-x*(1+y)/(1-y)). - Vladimir Kruchinin, Apr 21 2015