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Expansion of 1/((1-x^2)*(1-x^4)^2*(1-x^6)*(1-x^8)*(1-x^10)) (even powers only).
(Formerly M2348 N0927)
1

%I M2348 N0927 #26 Sep 28 2023 14:07:44

%S 1,1,3,4,8,11,18,24,36,47,66,84,113,141,183,225,284,344,425,508,617,

%T 729,872,1020,1205,1397,1632,1877,2172,2480,2846,3228,3677,4146,4691,

%U 5261,5917,6603,7386,8205,9133,10103,11195,12336,13613,14947,16431,17981,19697

%N Expansion of 1/((1-x^2)*(1-x^4)^2*(1-x^6)*(1-x^8)*(1-x^10)) (even powers only).

%D A. Cayley, Calculation of the minimum N.G.F. of the binary seventhic, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 10, p. 408-419.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001994/b001994.txt">Table of n, a(n) for n = 0..1000</a>

%H A. Cayley, <a href="/A001993/a001993.pdf">Calculation of the minimum N.G.F. of the binary seventhic</a>, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 10, p. 408-419. [Annotated scanned copy]

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9, -33, 63, -66, 36, -8).

%t nn = 202; t = CoefficientList[Series[1/((1 - x^2)*(1 - x^4)^2*(1 - x^6)*(1 - x^8)*(1 - x^10)), {x, 0, nn}], x]; t = Take[t, {1, nn, 2}]

%Y Cf. A001996.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Feb 09 2000