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

0,5

Comments

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

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A004695, A032443, A077864.

Sequence in context: A334844 A296457 A124020 * A135226 A104730 A249488

Adjacent sequences: A124231 A124232 A124233 * A124235 A124236 A124237

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 22 2006

Status

approved