A296387 a(0) = a(1) = 1; a(n) = [x^n] Product_{k=1..n-1} (1 + x^a(k))/(1 - x^a(k)).

1, 1, 2, 6, 8, 10, 14, 18, 26, 34, 46, 58, 74, 90, 114, 138, 174, 210, 260, 310, 378, 446, 536, 626, 748, 870, 1034, 1198, 1410, 1622, 1892, 2162, 2510, 2858, 3306, 3754, 4316, 4878, 5576, 6274, 7144, 8014, 9096, 10178, 11508, 12838, 14458, 16078, 18048, 20018, 22410, 24802, 27690, 30578, 34040

Offset

0,3

Links

Table of n, a(n) for n=0..54.

Index entries for sequences related to partitions

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = -x - 2*x^2 + Product_{n>=1} (1 + x^a(n))/(1 - x^a(n)).

Mathematica

a[n_] := a[n] = SeriesCoefficient[Product[(1 + x^a[k])/(1 - x^a[k]), {k, 1, n - 1}], {x, 0, n}]; a[0] = a[1] = 1; Table[a[n], {n, 0, 54}]

Crossrefs

Cf. A015128, A151945, A229362, A293806.

Sequence in context: A036554 A260400 A370597 * A302658 A324175 A358428

Adjacent sequences: A296384 A296385 A296386 * A296388 A296389 A296390

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 11 2017

Status

approved