A383023 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) is the n-th term of the inverse Weigh transform of j-> k^j.
1, 2, 1, 3, 3, 0, 4, 6, 2, 1, 5, 10, 8, 6, 0, 6, 15, 20, 24, 6, 0, 7, 21, 40, 70, 48, 11, 0, 8, 28, 70, 165, 204, 124, 18, 1, 9, 36, 112, 336, 624, 690, 312, 36, 0, 10, 45, 168, 616, 1554, 2620, 2340, 834, 56, 0, 11, 55, 240, 1044, 3360, 7805, 11160, 8230, 2184, 105, 0
Offset: 1
Examples
Square array begins: 1, 2, 3, 4, 5, 6, 7, ... 1, 3, 6, 10, 15, 21, 28, ... 0, 2, 8, 20, 40, 70, 112, ... 1, 6, 24, 70, 165, 336, 616, ... 0, 6, 48, 204, 624, 1554, 3360, ... 0, 11, 124, 690, 2620, 7805, 19656, ... 0, 18, 312, 2340, 11160, 39990, 117648, ...
Links
- Christian G. Bower, PARI programs for transforms, 2007.
- N. J. A. Sloane, Maple programs for transforms, 2001-2020.
Formula
A(n,k) = (1/n) * (k^n + Sum_{d
Product_{n>=1} (1 + x^n)^A(n,k) = 1/(1 - k*x).