A069950 -id:A069950 - cp's OEIS frontend

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

N. J. A. Sloane, May 05 2002

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).

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

Cf. A008763, A069950.

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

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

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 *)

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

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

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

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

Original entry on oeis.org

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

N. J. A. Sloane, May 05 2002

nonn

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).

Cf. A069950.

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

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 *)

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

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

cp's OEIS Frontend

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

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

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cp's OEIS Frontend

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

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

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