A124234 Riordan array (1/(1-x), x(1+x)^2).

1, 1, 1, 1, 3, 1, 1, 4, 5, 1, 1, 4, 11, 7, 1, 1, 4, 15, 22, 9, 1, 1, 4, 16, 42, 37, 11, 1, 1, 4, 16, 57, 93, 56, 13, 1, 1, 4, 16, 63, 163, 176, 79, 15, 1, 1, 4, 16, 64, 219, 386, 299, 106, 17, 1, 1, 4, 16, 64, 247, 638, 794, 470, 137, 19, 1

Offset: 0

Author

Paul Barry, Oct 22 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A077864. Diagonal sums are A004695(n+3). T(2n,n) is A032443.

Examples

			Triangle begins
1,
1, 1,
1, 3, 1,
1, 4, 5, 1,
1, 4, 11, 7, 1,
1, 4, 15, 22, 9, 1,
1, 4, 16, 42, 37, 11, 1
		

Crossrefs

Cf. A004695, A032443, A077864.

Programs

PARI

tabl(nn) = for (n=0, nn, for (k=0, n, print1(sum(j=0, n-k, binomial(2*k, j)), ", ")); print();); \\ Michel Marcus, Nov 05 2016

Formula

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