A255961 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is Euler transform of (j->j*k).
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 7, 6, 0, 1, 4, 12, 18, 13, 0, 1, 5, 18, 37, 47, 24, 0, 1, 6, 25, 64, 111, 110, 48, 0, 1, 7, 33, 100, 215, 303, 258, 86, 0, 1, 8, 42, 146, 370, 660, 804, 568, 160, 0, 1, 9, 52, 203, 588, 1251, 1938, 2022, 1237, 282, 0
Offset: 0
Examples
Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, 1, 1, ... 0, 1, 2, 3, 4, 5, 6, 7, ... 0, 3, 7, 12, 18, 25, 33, 42, ... 0, 6, 18, 37, 64, 100, 146, 203, ... 0, 13, 47, 111, 215, 370, 588, 882, ... 0, 24, 110, 303, 660, 1251, 2160, 3486, ... 0, 48, 258, 804, 1938, 4005, 7459, 12880, ... 0, 86, 568, 2022, 5400, 12150, 24354, 44885, ...
Links
- Alois P. Heinz, Rows n = 0..140, flattened
Crossrefs
Programs
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Maple
A:= proc(n, k) option remember; `if`(n=0, 1, k*add( A(n-j, k)*numtheory[sigma][2](j), j=1..n)/n) end: seq(seq(A(n, d-n), n=0..d), d=0..12); -
Mathematica
A[n_, k_] := A[n, k] = If[n==0, 1, k*Sum[A[n-j, k]*DivisorSigma[2, j], {j, 1, n}]/n]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Feb 02 2016, after Alois P. Heinz *)
Formula
G.f. of column k: Product_{j>=1} 1/(1-x^j)^(j*k).
T(n,k) = Sum_{i=0..k} C(k,i) * A257673(n,k-i).
Comments