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A334781
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Array read by antidiagonals: T(n,k) = Sum_{i=1..n} binomial(1+i,2)^k.
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7
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0, 0, 1, 0, 1, 2, 0, 1, 4, 3, 0, 1, 10, 10, 4, 0, 1, 28, 46, 20, 5, 0, 1, 82, 244, 146, 35, 6, 0, 1, 244, 1378, 1244, 371, 56, 7, 0, 1, 730, 8020, 11378, 4619, 812, 84, 8, 0, 1, 2188, 47386, 108020, 62003, 13880, 1596, 120, 9, 0, 1, 6562, 282124, 1047386, 867395, 256484, 35832, 2892, 165, 10
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OFFSET
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0,6
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..1325
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FORMULA
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T(n,k) = Sum_{i=0..2*(k-1)} A154283(k,i) * binomial(n+2+i, 2*k+i) for k > 0.
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EXAMPLE
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Array begins:
===============================================================
n\k | 0 1 2 3 4 5 6 7
----|----------------------------------------------------------
0 | 0 0 0 0 0 0 0 0 ...
1 | 1 1 1 1 1 1 1 1 ...
2 | 2 4 10 28 82 244 730 2188 ...
3 | 3 10 46 244 1378 8020 47386 282124 ...
4 | 4 20 146 1244 11378 108020 1047386 10282124 ...
5 | 5 35 371 4619 62003 867395 12438011 181141499 ...
6 | 6 56 812 13880 256484 4951496 98204132 1982230040 ...
7 | 7 84 1596 35832 871140 22161864 580094436 15475158552 ...
...
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PROG
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(PARI) T(n, k) = {sum(i=1, n, binomial(1+i, 2)^k)}
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CROSSREFS
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Columns k=0..7 are A001477, A000292, A024166, A085438, A085439, A085440, A085441, A085442.
Rows n=0..3 are A000004, A000012, A034472, A074508.
Main diagonal is A249564(n > 0).
Cf. A154283 (coefficients).
Sequence in context: A124912 A138752 A342133 * A291656 A209063 A342321
Adjacent sequences: A334778 A334779 A334780 * A334782 A334783 A334784
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KEYWORD
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nonn,tabl
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AUTHOR
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Andrew Howroyd, May 15 2020
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STATUS
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approved
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