A090299 Table T(n,k), n>=0 and k>=0, read by antidiagonals : the k-th column given by the k-th polynomial K_k related to A090285.

1, 1, 1, 2, 3, 1, 5, 10, 5, 1, 14, 35, 22, 7, 1, 42, 126, 93, 38, 9, 1, 132, 462, 386, 187, 58, 11, 1, 429, 1716, 1586, 874, 325, 82, 13, 1, 1430, 6435, 6476, 3958, 1686, 515, 110, 15, 1, 4862, 24310, 26333, 17548, 8330, 2934, 765, 142, 17, 1

Offset: 0

Author

Philippe Deléham, Jan 25 2004

Keywords

• easy
• nonn
• tabl

Comments

Read as a number triangle, this is the Riordan array (c(x),x/sqrt(1-4x)) where c(x) is the g.f. of A000108. - Paul Barry, May 16 2005

Examples

			row n=0 : 1, 1, 2, 5, 14, 42, 132, 429, ... see A000108.
row n=1 : 1, 3, 10, 35, 126, 462, 1716, 6435, ... see A001700.
row n=2 : 1, 5, 22, 93, 386, 1586, 6476, ... see A000346.
row n=3 : 1, 7, 38, 187, 874, 3958, 17548, ... see A000531.
row n=4 : 1, 9, 58, 325, 1686, 8330, 39796, ... see A018218.
		

Crossrefs

Other rows : A029887, A042941, A045724, A042985, A045492. Columns : A000012, A005408. Row n is the convolution of the row (n-j) with A000984, A000302, A002457, A002697 (first term omitted), A002802, A038845, A020918, A038846, A020920 for j=1, 2, ..9 respectively.

Formula

T(n, k) = K_k(n)= Sum_{j>=0} A090285(k, j)*2^j*binomial(n, j). T(n, 1) = 2*n+1. T(n, 2) = 2*A028387(n).

Extensions

Corrected by Alford Arnold, Oct 18 2006