A365540 Antidiagonal sums of A365539.

0, 1, 5, 12, 24, 39, 61, 86, 118, 155, 199, 246, 304, 365, 433, 508, 592, 679, 777, 878, 990, 1109, 1235, 1364, 1508, 1657, 1813, 1976, 2150, 2327, 2519, 2714, 2920, 3133, 3353, 3580, 3824, 4071, 4325, 4586, 4862, 5141, 5435, 5732, 6040, 6359, 6685, 7014, 7362

Offset: 0

Author

Stefano Spezia, Sep 08 2023

Keywords

• nonn

Crossrefs

Cf. A000005, A114003 (2nd differences), A365539.

Programs

Mathematica

A365539[n_,k_]:=SeriesCoefficient[(1+x^k)/((1-x)^2*(1-x^k)),{x,0,n}]; Table[Sum[A365539[n-k,k], {k,n}], {n,0,48}] (* or *)
Table[Sum[Sum[2  DivisorSigma[0,k]-1,{k,m}],{m,n}],{n,0,48}]

Formula

a(n) = Sum_{m=1..n} (Sum_{k=1..m} (2*A000005(k) - 1)).