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

0,6

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325

Formula

T(n,k) = Sum_{i=0..2*(k-1)} A154283(k,i) * binomial(n+2+i, 2*k+i) for k > 0.

Example

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 ...
  ...

Prog

(PARI) T(n, k) = {sum(i=1, n, binomial(1+i, 2)^k)}

Crossrefs

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: A368506 A342133 A358050 * A291656 A209063 A342321

Adjacent sequences: A334778 A334779 A334780 * A334782 A334783 A334784

Keyword

nonn,tabl

Author

Andrew Howroyd, May 15 2020

Status

approved