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%I #14 Sep 08 2022 08:45:03
%S 13,223,1577,7018,23431,64316,153190,327718,644573,1185025,2061259,
%T 3423422,5467399,8443318,12664784,18518842,26476669,37104995,51078253,
%U 69191458,92373815,121703056,158420506,203946878,259898797,328106053
%N Seventh 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="/A062127/b062127.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: (2*x^6 + 14*x^5 + 72*x^4 + 207*x^3 + 289*x^2 + 132*x + 13)/(1-x)^7. 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) = (81*n^6 + 567*n^5 + 2205*n^4 + 4545*n^3 + 5674*n^2 + 3728*n + 1040)/80.
%F E.g.f.: (1040 + 16800*x + 45760*x^2 + 39240*x^3 + 13140*x^4 + 1782*x^5 + 81*x^6)*exp(x)/80. (End)
%t Table[(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80, {n, 0, 40}] (* _G. C. Greubel_, Jan 31 2019 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{13,223,1577,7018,23431,64316,153190},30] (* _Harvey P. Dale_, Jun 07 2022 *)
%o (PARI) vector(40, n, n--; (81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80) \\ _G. C. Greubel_, Jan 31 2019
%o (Magma) [(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80: n in [0..40]]; // _G. C. Greubel_, Jan 31 2019
%o (Sage) [(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80 for n in range(40)] # _G. C. Greubel_, Jan 31 2019
%o (GAP) List([0..40], n -> (81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80); # _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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