A045842 Expansion of Product_{k>=0} 1/(1 - x^(k+1))^A001156(k).

1, 1, 2, 3, 5, 8, 13, 19, 29, 43, 65, 94, 138, 197, 284, 403, 571, 801, 1124, 1562, 2170, 2992, 4118, 5636, 7700, 10467, 14201, 19189, 25873, 34763, 46614, 62305, 83113, 110565, 146791, 194408, 256985, 338934, 446211, 586231, 768855, 1006450, 1315304, 1715882, 2234957, 2906250

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Transforms

Formula

G.f.: Product_{k>=0} 1/(1 - x^(k+1))^A001156(k).

Example

1/((1-x)^1 * (1-x^2)^1 * (1-x^3)^1 * (1-x^4)^1 * (1-x^5)^2 * (1-x^6)^2 * (1-x^7)^2 * (1-x^8)^2 * (1-x^9)^3 * ...) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 13*x^6 + 19*x^7 + 29*x^8 + 43*x^9 + ... .

Crossrefs

Cf. A001156.

Sequence in context: A308994 A326469 A326594 * A324741 A200462 A088795

Adjacent sequences: A045839 A045840 A045841 * A045843 A045844 A045845

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Seiichi Manyama, Nov 10 2018

Status

approved