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A347823
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Triangle read by rows: T(n,k) = (n+k+1)*binomial(n,k), 0 <= k <= n.
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1
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1, 2, 3, 3, 8, 5, 4, 15, 18, 7, 5, 24, 42, 32, 9, 6, 35, 80, 90, 50, 11, 7, 48, 135, 200, 165, 72, 13, 8, 63, 210, 385, 420, 273, 98, 15, 9, 80, 308, 672, 910, 784, 420, 128, 17, 10, 99, 432, 1092, 1764, 1890, 1344, 612, 162, 19, 11, 120, 585, 1680, 3150, 4032, 3570, 2160, 855, 200, 21
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OFFSET
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0,2
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LINKS
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FORMULA
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Row g.f.: (1 + x)^(n-1)*(1 + n + x + 2*n*x). - Stefano Spezia, Jan 23 2022
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EXAMPLE
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Triangle begins:
1;
2, 3;
3, 8, 5;
4, 15, 18, 7;
5, 24, 42, 32, 9;
6, 35, 80, 90, 50, 11;
7, 48, 135, 200, 165, 72, 13;
8, 63, 210, 385, 420, 273, 98, 15;
...
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PROG
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(PARI) T(n, k) = (n+k+1)*binomial(n, k) \\ Andrew Howroyd, Jan 23 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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