A088931 G.f.: Sum_{n >= 1} ( x^(2^n)/ ((1+x^(2^(n-1)))*Product_{j=0..n-1} (1-x^(2^j)) ) ).

0, 0, 1, 0, 2, 1, 2, 1, 4, 3, 5, 4, 7, 6, 8, 7, 12, 11, 15, 14, 20, 19, 24, 23, 31, 30, 37, 36, 45, 44, 52, 51, 64, 63, 75, 74, 90, 89, 104, 103, 124, 123, 143, 142, 167, 166, 190, 189, 221, 220, 251, 250, 288, 287, 324, 323, 369, 368, 413, 412, 465, 464, 516, 515, 580

Offset

0,5

Comments

This is the g.f. for the number of non-squashing partitions with a repeated part, that is, A000123(n) - A088567(n).

Links

Table of n, a(n) for n=0..64.

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

Example

x^2/((1 + x)*(1 - x)) + x^4/((1 + x^2)*(1 - x)*(1 - x^2)) + x^8/((1 + x^4)*(1 - x)*(1 - x^2)*(1 - x^4)) + ...

Mathematica

max = 65; Sum[x^(2^n)/((1+x^(2^(n-1))) Product[1-x^(2^j), {j, 0, n-1}]), {n, 1, Log[2, max] // Ceiling}] + O[x]^(max) // CoefficientList[#, x]& (* Jean-François Alcover, Oct 05 2018 *)

Crossrefs

Apart from initial terms, same as A088980.

Sequence in context: A344255 A344256 A344257 * A088980 A254436 A208548

Adjacent sequences: A088928 A088929 A088930 * A088932 A088933 A088934

Keyword

nonn

Author

N. J. A. Sloane, Dec 02 2003

Status

approved