A060962 Expansion of (1+x^2)*(1+x^5)/( Product_{j=1..7} (1-x^j) ).

1, 1, 3, 4, 7, 11, 17, 25, 36, 50, 69, 93, 125, 163, 213, 272, 346, 435, 543, 671, 825, 1005, 1218, 1466, 1756, 2090, 2478, 2921, 3430, 4009, 4669, 5414, 6259, 7207, 8274, 9468, 10803, 12289, 13944, 15777, 17809, 20052, 22528, 25249, 28243, 31522, 35115, 39041, 43327, 47995, 53078

Offset: 0

Author

N. J. A. Sloane, May 05 2002

Keywords

• nonn
• easy

References

• G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis VIII: Plane partition diamonds, Advances Applied Math., 27 (2001), 231-242 (Cor. 2.1, n=2).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A008763, A069950.

Programs

Magma

R:=PowerSeriesRing(Integers(), 55); Coefficients(R!( (1+x^2)*(1+x^5)/( &*[1-x^j: j in [1..7]] ) )); // G. C. Greubel, Jan 15 2020

Maple

seq(coeff(series((1+x^2)*(1+x^5)/(mul(1-x^j, j=1..7)), x, n+1), x, n), n = 0..55); # G. C. Greubel, Jan 15 2020

Mathematica

Table[SeriesCoefficient[(1+x^2)*(1+x^5)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5)/(1-x^6)/(1-x^7),{x,0,n}],{n,0,55}] (* Vaclav Kotesovec, Oct 01 2012 *)

PARI

Vec((1+x^2)*(1+x^5)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5)/(1-x^6)/(1-x^7) +O(x^55)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

def A060962_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)*(1+x^5)/(product(1-x^j for j in (1..7))) ).list()
A060962_list(55) # G. C. Greubel, Jan 15 2020

Formula

a(n) = 1 - 263117*n/1814400 + 109537*n^2/907200 + 97*n^3/4320 + 127*n^4/72576 + n^5/14400 + n^6/907200 + 4/7*floor(n/7) + 1/3*floor(n/6) + 2/25*floor(n/5) - 11/162*floor(n/3) + (73/192 + 5*n/96)*floor(n/2) + 1/7*floor((1+n)/7) - 1/6*floor((1+n)/6) + 4/25*floor((1+n)/5) + (53/162 + n/54)*floor((1+n)/3) + 3/7*floor((2+n)/7) - 4/25*floor((2+n)/5) + 2/7*floor((3+n)/7) + 8/25*floor((3+n)/5) + 1/7*floor((4+n)/7) + 3/7*floor((5+n)/7). - Vaclav Kotesovec, Sep 29 2012