A012001 - OEIS

%I #20 Apr 12 2017 23:09:22

%S 0,1,2,46,1112,55816,3804272,372397936,47682319232,7841034902656,

%T 1601250315636992,398250217200414976,118406090377889303552,

%U 41478295178427681104896,16904918898000336224294912

%N E.g.f.: -tan(log(cos(x))), even powers only.

%C The highest power of 2 dividing a(n) appears to be A011371(n). The odd part starts 1, 1, 23, 139, 6977, 237767, 23274871, 372518119, 61258085177,.... - _Ralf Stephan_, Aug 14 2013

%H G. C. Greubel, <a href="/A012001/b012001.txt">Table of n, a(n) for n = 0..235</a>

%e -tan(log(cos(x))) = 1/2!*x^2 + 2/4!*x^4 + 46/6!*x^6 + 1112/8!*x^8 + ...

%t With[{nn = 50}, Take[CoefficientList[Series[-Tan[Log[Cos[x]]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* _G. C. Greubel_, Apr 12 2017 *)

%o (PARI) a(n)={n*=2; my(x='x+O('x^(n+1))); polcoeff( serlaplace( -tan(log(cos(x)))), n); } \\ _Ralf Stephan_, Aug 14 2013

%K nonn

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Checked by _N. J. A. Sloane_, Dec 16 2011