A321286 Expansion of Product_{1 <= i < j} (1 + x^(i*j)).

1, 0, 1, 1, 1, 2, 3, 3, 5, 6, 8, 10, 14, 16, 22, 28, 33, 43, 55, 64, 84, 102, 123, 153, 188, 224, 277, 335, 401, 486, 589, 695, 843, 1006, 1191, 1428, 1698, 1999, 2384, 2814, 3312, 3914, 4612, 5395, 6355, 7447, 8691, 10182, 11892, 13826, 16146, 18770, 21779, 25313

Offset

0,6

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{k>0} (1 + x^k)^A056924(k).

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 + x^k)^Floor[DivisorSigma[0, k]/2], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 02 2018 *)
nmax = 100; A056924 = Table[Floor[DivisorSigma[0, k]/2], {k, 1, nmax}]; s = 1; Do[s *= Sum[Binomial[A056924[[k]], j]*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]]; , {k, 2, nmax}]; Take[CoefficientList[s, x], nmax+1] (* Vaclav Kotesovec, Nov 02 2018 *)

Crossrefs

Cf. A056924, A107742, A211856, A321285.

Sequence in context: A241068 A035938 A024503 * A061790 A107236 A192184

Adjacent sequences: A321283 A321284 A321285 * A321287 A321288 A321289

Keyword

nonn

Author

Seiichi Manyama, Nov 02 2018

Status

approved