A090299 - OEIS

%I #10 Feb 22 2013 14:38:55

%S 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,

%T 58,11,1,429,1716,1586,874,325,82,13,1,1430,6435,6476,3958,1686,515,

%U 110,15,1,4862,24310,26333,17548,8330,2934,765,142,17,1

%N 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.

%C 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

%F 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).

%e row n=0 : 1, 1, 2, 5, 14, 42, 132, 429, ... see A000108.

%e row n=1 : 1, 3, 10, 35, 126, 462, 1716, 6435, ... see A001700.

%e row n=2 : 1, 5, 22, 93, 386, 1586, 6476, ... see A000346.

%e row n=3 : 1, 7, 38, 187, 874, 3958, 17548, ... see A000531.

%e row n=4 : 1, 9, 58, 325, 1686, 8330, 39796, ... see A018218.

%Y 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.

%K easy,nonn,tabl

%O 0,4

%A _Philippe Deléham_, Jan 25 2004

%E Corrected by Alford Arnold, Oct 18 2006