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A117487
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G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5))^2.
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5
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1, 2, 5, 10, 20, 36, 63, 104, 169, 264, 405, 604, 888, 1278, 1815, 2536, 3502, 4772, 6437, 8586, 11352, 14866, 19315, 24890, 31851, 40466, 51089, 64092, 79952, 99172, 122386, 150264, 183639, 223394, 270605, 326422, 392225, 469490, 559970, 665542, 788412
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OFFSET
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1,2
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COMMENTS
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Molien series for S_5 X S_5, cf. A001401.
Molien series for S_k X S_k approaches A000712 as k increases.
Note that a(5) is 20, the scalar product of (1 1 2 3 5) and (5 3 2 1 1 ). a(6) is 36, the scalar product of (1 1 2 3 5 7) and (7 5 3 2 1 1 ).
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LINKS
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MAPLE
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# adapted from A115994 kmax := 120 : qmax := kmax/2 : g:=sum(t^k*q^(k^2)/product((1-q^j)^2, j=1..k), k=1..kmax): gser:=series(g, q=0, qmax): for n from 25 to qmax-1 do P :=coeff(gser, q^n) : printf("%a, ", coeff(P, t^5)); od: # R. J. Mathar, Apr 07 2006
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MATHEMATICA
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CoefficientList[Series[1/(Product[(1-x^j), {j, 5}])^2, {x, 0, 45}], x] (* G. C. Greubel, Jan 01 2020 *)
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PROG
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(Magma) n:=5; G:=SymmetricGroup(n); H:=DirectProduct(G, G); MolienSeries(H); // N. J. A. Sloane
(PARI) my(x='x+O('x^45)); Vec( 1/(prod(j=1, 5, 1-x^j))^2 ) \\ G. C. Greubel, Jan 01 2020
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(product(1-x^j for j in (1..5)))^2 ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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