A069957 Expansion of 1/((1-x)^2*(1-x^2)^2*(1-x^3)*(1-x^4)^2*(1-x^5)).

1, 2, 5, 9, 18, 30, 51, 79, 124, 183, 270, 382, 540, 740, 1010, 1347, 1789, 2333, 3028, 3873, 4932, 6205, 7772, 9637, 11901, 14571, 17770, 21512, 25948, 31098, 37143, 44113, 52226, 61522, 72258, 84489, 98519, 114418, 132540, 152976, 176139, 202141

Offset: 0

Author

N. J. A. Sloane, May 05 2002

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis VIII: Plane partition diamonds, Advances Applied Math., 27 (2001), 231-242.
• Index entries for linear recurrences with constant coefficients, signature (2, 1, -3, 1, -2, -1, 4, 2, 0, -2, -2, -2, 0, 2, 4, -1, -2, 1, -3, 1, 2, -1).

Crossrefs

Cf. A069950.

Programs

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x^3)*(1-x^5)/(&*[1-x^j: j in [1..5]])^2 )); // G. C. Greubel, Aug 17 2022

Mathematica

CoefficientList[Series[1/((1 - x)^2 (1 - x^2)^2 (1 - x^3) (1 - x^4)^2 (1 - x^5)), {x, 0, 60}], x] (* Vincenzo Librandi, Sep 05 2016 *)

Sage

def A069957_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x^3)*(1-x^5)/(product(1-x^j for j in (1..5)))^2 ).list()
A069957_list(60) # G. C. Greubel, Aug 17 2022

Formula

G.f.: (1-x^3)*(1-x^5)/( Product_{j=1..5} 1-x^j )^2. - G. C. Greubel, Aug 17 2022