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%I #10 Sep 08 2022 08:45:03
%S 8,114,667,2504,7191,17266,36482,70050,124882,209834,335949,516700,
%T 768233,1109610,1563052,2154182,2912268,3870466,5066063,6540720,
%U 8340715,10517186,13126374,16229866,19894838,24194298,29207329
%N Sixth column of A046741.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (2.3.14).
%H G. C. Greubel, <a href="/A062126/b062126.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: (x+2)*(2*x^4 + 8*x^3 + 36*x^2 + 31*x + 4)/(1-x)^6. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1 - y - y^2)*(1-y) - (1+y)*x).
%F From _G. C. Greubel_, Jan 31 2019: (Start)
%F a(n) = (320 + 1114*n + 1515*n^2 + 1125*n^3 + 405*n^4 + 81*n^5)/40.
%F E.g.f.: (320 + 4240*x + 8940*x^2 + 5580*x^3 + 1215*x^4 + 81*x^5)*exp(x)/40. (End)
%t Table[(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40, {n, 0, 40}] (* _G. C. Greubel_, Jan 31 2019 *)
%o (PARI) vector(40, n, n--; (320+1114*n+1515*n^2+1125*n^3+405*n^4 + 81*n^5)/40) \\ _G. C. Greubel_, Jan 31 2019
%o (Magma) [(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40: n in [0..40]]; // _G. C. Greubel_, Jan 31 2019
%o (Sage) [(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40 for n in range(40)] # _G. C. Greubel_, Jan 31 2019
%o (GAP) List([0..40], n -> (320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5 )/40); # _G. C. Greubel_, Jan 31 2019
%Y Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062123-A062127.
%K easy,nonn
%O 0,1
%A _Vladeta Jovovic_, Jun 04 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001
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