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 A096583 Symmetric square array T(n,k)=T(k,n), read by antidiagonals, such that the n-th diagonal equals the convolution of the n-th row with the antidiagonal sums, with T(0,n)=1, for n>=0. 2
 1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 8, 7, 1, 1, 9, 16, 16, 9, 1, 1, 11, 23, 20, 23, 11, 1, 1, 13, 35, 44, 44, 35, 13, 1, 1, 15, 46, 69, 44, 69, 46, 15, 1, 1, 17, 62, 99, 108, 108, 99, 62, 17, 1, 1, 19, 77, 147, 179, 96, 179, 147, 77, 19, 1, 1, 21, 97, 206, 272, 248, 248, 272, 206, 97, 21 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The main diagonal (A096585) equals the partial sums of the antidiagonal sums (A096584). LINKS EXAMPLE Antidiagonal sums are A096584 = [1,2,5,12,24,52,90,186,306,574,...]; convolution of antidiagonal sums and first row yields main diagonal: A096585 = [1,3,8,20,44,96,186,372,678,...]; convolution of antidiagonal sums and second row yields secondary diagonal: [1,5,16,44,108,248,530,1088,2138,4068,...]. Rows begin: [1,1,1,1,1,1,1,1,1,...], [1,3,5,7,9,11,13,15,17,...], [1,5,8,16,23,35,46,62,77,...], [1,7,16,20,44,69,99,147,206,...], [1,9,23,44,44,108,179,272,379,...], [1,11,35,69,108,96,248,429,669,...], [1,13,46,99,179,248,186,530,965,...], [1,15,62,147,272,429,530,372,1088,...], [1,17,77,206,379,669,965,1088,678,...],... PROG (PARI) {T(n, k)=if(n<0|k<0, 0, if(n==0|k==0, 1, if(n>k, sum(j=0, k, T(n-k, j)*sum(i=0, k-j, T(k-j-i, i))), sum(j=0, n, T(k-n, j)*sum(i=0, n-j, T(n-j-i, i))); ); ))} CROSSREFS Cf. A096584, A096585. Sequence in context: A026703 A122917 A211315 * A130154 A208328 A134398 Adjacent sequences:  A096580 A096581 A096582 * A096584 A096585 A096586 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Jun 28 2004 STATUS approved

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