A302580 Numbers k such that the coefficient of x^k in the expansion of Ramanujan's function R(x) = Sum_{i>=0} x^(i*(i+1)/2)/Product_{j=1..i} (1 + x^j) is zero.

6, 9, 11, 16, 20, 21, 23, 27, 29, 30, 31, 33, 34, 36, 37, 38, 41, 44, 46, 49, 53, 56, 58, 59, 60, 61, 63, 64, 65, 66, 71, 72, 79, 80, 81, 82, 85, 86, 91, 93, 94, 96, 97, 98, 102, 104, 106, 107, 110, 111, 114, 115, 116, 120, 121, 122, 124, 128, 129, 131, 133, 135, 136, 137, 141, 142, 146, 148

Offset: 1

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• nonn

Comments

Numbers k such that number of partitions of k into distinct parts with even rank equals number of partitions of k into distinct parts with odd rank (the rank of a partition is its largest part minus the number of parts).

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A003406, A117192, A117193.

Programs

Mathematica

Flatten[Position[nmax = 150; Rest[CoefficientList[Series[Sum[x^(i (i + 1)/2)/Product[(1 + x^j), {j, 1, i}], {i, 0, nmax}], {x, 0, nmax}], x]], 0]]