A334781 Array read by antidiagonals: T(n,k) = Sum_{i=1..n} binomial(1+i,2)^k.
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
Offset: 0
Examples
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 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325
Crossrefs
Programs
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PARI
T(n,k) = {sum(i=1, n, binomial(1+i,2)^k)}
Formula
T(n,k) = Sum_{i=0..2*(k-1)} A154283(k,i) * binomial(n+2+i, 2*k+i) for k > 0.