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%I #15 Nov 05 2021 18:40:07
%S 0,1,63,6306,990550,227890755,72524317341,30560156566660,
%T 16483798503292716,11080974333713379525,9085235508141504416155,
%U 8924963654575108415598246,10349560274697013067017980738,13989200573862071630368836403591,21802322447828101388917112243376825
%N a(n) = E(2n,n)/2, where E(n,x) is the Euler polynomial.
%C Conjecture. For n >= 2, a(n) is divisible by n(n-1)/2, moreover, for odd n, a(n) is divisible by n^2(n-1)/2.
%D M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
%F a(n) = (-1)^n*(1^(2*n) - 2^(2*n) + ... +(-1)^n*(n-1)^(2*n)).
%F a(n) ~ c * n^(2*n), where c = A349003/2 = 1/(1 + exp(2)) = 0.1192029220221175559402708586976... - _Vaclav Kotesovec_, Nov 05 2021
%t Table[EulerE[2 n, n]/2, {n, 15}] (* _Michael De Vlieger_, Sep 23 2017 *)
%Y Cf. A291897, A291982.
%K nonn
%O 1,3
%A _Vladimir Shevelev_, Sep 23 2017
%E More terms from _Peter J. C. Moses_, Sep 23 2017