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%I #20 Aug 19 2018 14:39:32
%S 1,17,901,99917,18991081,5514615017,2270974911661,1258937450889317,
%T 903952433274722641,816101554527859690817,904827968753139590344021,
%U 1208617989532834039606507517,1914312457105234828011498655801,3547500444096776665586928259547417,7604155838367549221056955383942297981
%N Q_{2n+1}(sqrt(2))/sqrt(2) (see A104035).
%H G. C. Greubel, <a href="/A156138/b156138.txt">Table of n, a(n) for n = 0..207</a>
%F E.g.f.: sin(x)/(1 - 3*sin(x)^2) = x + 17*x^3/3! + 901*x^5/5! + 99917*x^7/7! + ... - _Peter Bala_, Feb 06 2017
%e G.f. = 1 + 17*x + 901*x^2 + 99917*x^3 + 18991081*x^4 + 5514615017*x^5 + ... - _Michael Somos_, Aug 19 2018
%p with(gfun):
%p series(sin(x)/(1-3*sin(x)^2), x, 30):
%p L := seriestolist(%):
%p seq(op(2*i, L)*(2*i-1)!, i = 1..floor((1/2)*nops(L)));
%p # _Peter Bala_, Feb 06 2017
%t With[{nmax = 50}, CoefficientList[Series[Sin[x]/(1 - 3*Sin[x]^2), {x, 0, nmax}], x]*Range[0, nmax]!][[2 ;; ;; 2]] (* _G. C. Greubel_, Aug 17 2018 *)
%o (PARI) x='x+O('x^50); v=Vec(serlaplace(sin(x)/(1 - 3*sin(x)^2))); vector((#v-1)\2 ,n,v[2*n-1]) \\ _G. C. Greubel_, Aug 17 2018
%Y Cf. A101923, A000364, A000464, A002439.
%Y Cf. other sequences with a g.f. of the form sin(x)/(1 - k*sin^2(x)): A101923 (k=1/2), A000364 (k=1), A000464 (k=2), A002439 (k=4).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 06 2009
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