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Generalized Euler numbers of type 3^2n.
(Formerly M2188)
0

%I M2188 #16 Dec 01 2018 07:58:25

%S 1,2,2248,54103952,9573516562048,7512502267832874752,

%T 19387585646491113265435648,134942950050961684035671842506752,

%U 2199105667698535717737352110310013698048

%N Generalized Euler numbers of type 3^2n.

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

%H Ira M. Gessel, <a href="http://dx.doi.org/10.1016/0097-3165(90)90060-A">Symmetric functions and P-recursiveness</a>, J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.

%F a(n) = (1/36^n) * Sum_{i=0..2*n} binomial(2*n, i) * A000364(n+i).

%t a[n_] := Sum[Binomial[2n, i]Abs[EulerE[2(n+i)]], {i, 0, 2n}]/36^n

%Y CF. A000364 (Euler numbers).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, _Simon Plouffe_

%E Edited by _Dean Hickerson_, Dec 10 2002