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E.g.f. (x*tan(x)-x^2)/8 (even powers only).
1

%I #11 Apr 27 2023 09:55:05

%S 0,0,1,12,272,9920,530688,39144448,3807514624,472197021696,

%T 72722212782080,13616619646091264,3046271659520557056,

%U 802494810618175946752,245880605613803859607552,86696940704285991905525760,34855851028500677184683245568

%N E.g.f. (x*tan(x)-x^2)/8 (even powers only).

%F a(n) = 2^(2*n-1) * (2^(2*n)-1) * abs(Bernoulli(2*n))/4 - (C(1,n) - C(0,n))/4.

%t With[{nn=40},Take[CoefficientList[Series[(x*Tan[x]-x^2)/8,{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, May 06 2014 *)

%Y Column k=2 of Euler triangle A117414.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Mar 13 2006

%E More terms from _Harvey P. Dale_, May 06 2014