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A154948
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Riordan array ((1+x)/(1-x^2)^2, x(1+x)/(1-x)).
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4
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1, 1, 1, 2, 3, 1, 2, 6, 5, 1, 3, 10, 14, 7, 1, 3, 15, 30, 26, 9, 1, 4, 21, 55, 70, 42, 11, 1, 4, 28, 91, 155, 138, 62, 13, 1, 5, 36, 140, 301, 363, 242, 86, 15, 1, 5, 45, 204, 532, 819, 743, 390, 114, 17, 1, 6, 55, 285, 876, 1652, 1925, 1375, 590, 146, 19, 1
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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Number triangle T(n,k) = Sum_{j=0..n+1} C(n+1-j,k+1)*C(k-1,j).
T(n, k) = binomial(n+1,k+1)*2F1(-(n-k), -(k-1); -(n+1); -1). - G. C. Greubel, Feb 18 2020
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EXAMPLE
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Triangle begins
1;
1, 1;
2, 3, 1;
2, 6, 5, 1;
3, 10, 14, 7, 1;
3, 15, 30, 26, 9, 1;
4, 21, 55, 70, 42, 11, 1;
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MAPLE
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seq(seq( add(binomial(k-1, j)*binomial(n-j+1, k+1), j=0..n+1), k=0..n), n=0..10); # G. C. Greubel, Feb 18 2020
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MATHEMATICA
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Table[Binomial[n+1, k+1]*Hypergeometric2F1[-n+k, -k+1, -n-1, -1], {n, 0, 5}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 18 2020 *)
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PROG
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(Magma) [ (&+[Binomial(k-1, j)*Binomial(n-j+1, k+1): j in [0..n+1]]): k in [0..n], n in [0..10]]; // G. C. Greubel, Feb 18 2020
(Sage) [[ sum(binomial(k-1, j)*binomial(n-j+1, k+1) for j in (0..n+1)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Feb 18 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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