A158687 Riordan array (1/(1-x),x(1+x)^2/(1-x)).

1, 1, 1, 1, 4, 1, 1, 8, 7, 1, 1, 12, 24, 10, 1, 1, 16, 56, 49, 13, 1, 1, 20, 104, 160, 83, 16, 1, 1, 24, 168, 400, 351, 126, 19, 1, 1, 28, 248, 832, 1120, 656, 178, 22, 1, 1, 32, 344, 1520, 2912, 2561, 1102, 239, 25, 1

Offset: 0

Author

Paul Barry, Mar 24 2009

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A077936. Diagonal sums are A129847. Central terms are A059304.

Inverse of alternating signed version is A100326.

Examples

			Number triangle begins
1,
1, 1,
1, 4, 1,
1, 8, 7, 1,
1, 12, 24, 10, 1,
1, 16, 56, 49, 13, 1,
1, 20, 104, 160, 83, 16, 1
		

Crossrefs

Cf. A059304, A077936, A100326, A129847.

Formula

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

T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k-1) + T(n-3,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, Nov 11 2013

G.f.: 1/(1-y-x*(1+y)^2). - Vladimir Kruchinin, Apr 21 2015