A368479 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} 2^j * j^k.
1, 0, 3, 0, 2, 7, 0, 2, 10, 15, 0, 2, 18, 34, 31, 0, 2, 34, 90, 98, 63, 0, 2, 66, 250, 346, 258, 127, 0, 2, 130, 714, 1274, 1146, 642, 255, 0, 2, 258, 2074, 4810, 5274, 3450, 1538, 511, 0, 2, 514, 6090, 18458, 24810, 19098, 9722, 3586, 1023
Offset: 0
Examples
Square array begins:
1, 0, 0, 0, 0, 0, 0, ...
3, 2, 2, 2, 2, 2, 2, ...
7, 10, 18, 34, 66, 130, 258, ...
15, 34, 90, 250, 714, 2074, 6090, ...
31, 98, 346, 1274, 4810, 18458, 71626, ...
63, 258, 1146, 5274, 24810, 118458, 571626, ...
127, 642, 3450, 19098, 107754, 616122, 3557610, ...
Links
- OEIS Wiki, Eulerian polynomials.
Crossrefs
Programs
-
PARI
T(n, k) = sum(j=0, n, 2^j*j^k);
Formula
G.f. of column k: 2*x*A_k(2*x)/((1-x) * (1-2*x)^(k+1)), where A_n(x) are the Eulerian polynomials for k > 0.