A368504 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^(n-j) * j^k.
1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 6, 1, 0, 1, 11, 21, 10, 1, 0, 1, 20, 60, 58, 15, 1, 0, 1, 37, 161, 244, 141, 21, 1, 0, 1, 70, 428, 900, 857, 318, 28, 1, 0, 1, 135, 1149, 3164, 4225, 2787, 685, 36, 1, 0, 1, 264, 3132, 10990, 18945, 18196, 8704, 1434, 45, 1
Offset: 0
Examples
Square array begins: 1, 0, 0, 0, 0, 0, 0, ... 1, 1, 1, 1, 1, 1, 1, ... 1, 3, 6, 11, 20, 37, 70, ... 1, 6, 21, 60, 161, 428, 1149, ... 1, 10, 58, 244, 900, 3164, 10990, ... 1, 15, 141, 857, 4225, 18945, 81565, ... 1, 21, 318, 2787, 18196, 102501, 536046, ...
Links
- OEIS Wiki, Eulerian polynomials.
Crossrefs
Programs
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PARI
T(n, k) = sum(j=0, n, k^(n-j)*j^k);
Formula
G.f. of column k: x*A_k(x)/((1-k*x) * (1-x)^(k+1)), where A_n(x) are the Eulerian polynomials for k > 0.
T(0,k) = 0^k; T(n,k) = k*T(n-1,k) + n^k.