This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117487 #20 Dec 30 2024 10:20:00
%S A117487 1,2,5,10,20,36,63,104,169,264,405,604,888,1278,1815,2536,3502,4772,
%T A117487 6437,8586,11352,14866,19315,24890,31851,40466,51089,64092,79952,
%U A117487 99172,122386,150264,183639,223394,270605,326422,392225,469490,559970,665542,788412
%N A117487 G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5))^2.
%C A117487 Molien series for S_5 X S_5, cf. A001401.
%C A117487 Molien series for S_k X S_k approaches A000712 as k increases.
%C A117487 Column 5 of table A115994.
%C A117487 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 ).
%H A117487 G. C. Greubel, <a href="/A117487/b117487.txt">Table of n, a(n) for n = 1..1000</a>
%H A117487 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -2, -1, -2, 0, 2, 6, 2, -3, -6, -5, -2, 3, 12, 3, -2, -5, -6, -3, 2, 6, 2, 0, -2, -1, -2, 1, 2, -1).
%p A117487 # 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
%t A117487 CoefficientList[Series[1/(Product[(1-x^j), {j,5}])^2, {x,0,45}], x] (* _G. C. Greubel_, Jan 01 2020 *)
%o A117487 (Magma) n:=5; G:=SymmetricGroup(n); H:=DirectProduct(G,G); MolienSeries(H); // _N. J. A. Sloane_
%o A117487 (PARI) my(x='x+O('x^45)); Vec( 1/(prod(j=1,5, 1-x^j))^2 ) \\ _G. C. Greubel_, Jan 01 2020
%o A117487 (Sage)
%o A117487 def A117487_list(prec):
%o A117487 P.<x> = PowerSeriesRing(ZZ, prec)
%o A117487 return P( 1/(product(1-x^j for j in (1..5)))^2 ).list()
%o A117487 A117487_list(45) # _G. C. Greubel_, Jan 01 2020
%Y A117487 Cf. A000027, A000712, A001399, A001400, A006918.
%Y A117487 Cf. A115994, A117485, A117486, A117488, A117489.
%K A117487 nonn
%O A117487 1,2
%A A117487 _Alford Arnold_, Mar 22 2006
%E A117487 More terms from _R. J. Mathar_, Apr 07 2006
%E A117487 Entry revised by _N. J. A. Sloane_, Mar 10 2007