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 A338934 Square array T(i,j) = Sum_{k=0...min(i,j)} C(i,k)*C(j,k)*C(2*k,k) (i>=0,j>=0), read by antidiagonals. 0
 1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 15, 7, 1, 1, 9, 31, 31, 9, 1, 1, 11, 53, 93, 53, 11, 1, 1, 13, 81, 213, 213, 81, 13, 1, 1, 15, 115, 411, 639, 411, 115, 15, 1, 1, 17, 155, 707, 1551, 1551, 707, 155, 17, 1, 1, 19, 201, 1121, 3239, 4653, 3239, 1121, 201, 19, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(i,j)*C(i+j,i) is the number of ways to write the vector (i,i,j,j) as a sum of vectors containing two occurrences of the number 1. Up to order, the number of different sums is A106255(i+1,j+1). LINKS EXAMPLE There are T(1,1)*C(2,1)=6 ways to write the vector (1,1,1,1) as a sum of vectors containing two occurrences of the number 1 : (1,1,0,0)+(0,0,1,1), (0,0,1,1)+(1,1,0,0), (1,0,1,0)+(0,1,0,1), (0,1,0,1)+(1,0,1,0), (1,0,0,1)+(0,1,1,0), (0,1,1,0)+(1,0,0,1). The square array T(i,j) (i >= 0, j >= 0) begins:   1,  1,  1,   1,    1,    1, ...   1,  3,  5,   7,    9,   11, ...   1,  5, 15,  31,   53,   81, ...   1,  7, 31,  93,  213,  411, ...   1,  9, 53, 213,  639, 1551, ...   1, 11, 81, 411, 1551, 4653, ...   ... MATHEMATICA T[i_, j_]:=Sum[Binomial[i, k]Binomial[j, k]Binomial[2k, k], {k, 0, Min[i, j]}]; Flatten[Table[T[i-j, j], {i, 0, 10}, {j, 0, i}]] (* Stefano Spezia, Nov 17 2020 *) CROSSREFS Central diagonal terms give A002893. Antidiagonal sums give A097893. Sequence in context: A108359 A100936 A086620 * A228356 A253670 A137897 Adjacent sequences:  A338931 A338932 A338933 * A338935 A338936 A338937 KEYWORD nonn,tabl AUTHOR Ludovic Schwob, Nov 16 2020 EXTENSIONS More terms from Stefano Spezia, Nov 17 2020 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)