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%I #30 Jun 25 2018 03:52:12
%S 0,-3,45,-1113,42585,-2348973,176992725,-17487754833,2195014332465,
%T -341282303124693,64397376340013805,-14499110277050234553,
%U 3840151029102915908745,-1182008039799685905580413,418424709061213506712209285,-168805428822414120140493978273
%N a(n) = -2^(2*n+1)*(E(2*n+1, 1/2) + E(2*n+1, 1) + 2*(E(2*n+2, 1/2) + E(2*n+2, 1))), where E(n,x) are the Euler polynomials.
%F a(n) = A240559(2*n+1) = (-1)^n*A147315(2*n+1,2) = (-1)^n*A186370(2*n,2*n-1).
%F a(n) = Sum_{k=0..2*n+1} (-1)^(2*n+1-k)*binomial(2*n+1, k)*2^k*(E(k, 1/2) + 2*E(k+1, 0)) where E(n,x) are the Euler polynomials.
%F a(n) = Sum_{k=0..2*n+1} (-1)^(2*n+1-k)*binomial(2*n+1, k)*(skp(k, 0) + skp(k+1, -1)), where skp(n, x) are the Swiss-Knife polynomials A153641.
%F a(n) = Bernoulli(2*n + 2) * 4^(n+1) * (1 - 4^(n+1)) / (2*n + 2) - EulerE(2*n + 2), where EulerE(2*n) is A028296. - _Daniel Suteu_, May 22 2018
%F a(n) = (-1)^(n+1) * (A000182(n+1) - A000364(n+1)). - _Daniel Suteu_, Jun 23 2018
%p A241242 := proc(n) e := n -> euler(n,1/2) + euler(n,1); -2^(2*n+1)*(e(2*n+1) + 2*e(2*n+2)) end: seq(A241242(n),n=0..15);
%t Array[-2^(2 # + 1)*(EulerE[2 # + 1, 1/2] + EulerE[2 # + 1, 1] + 2 (EulerE[2 # + 2, 1/2] + EulerE[2 # + 2, 1])) &, 16, 0] (* _Michael De Vlieger_, May 24 2018 *)
%Y Cf. A000182, A000364, A028296, A240559, A147315, A186370.
%K sign
%O 0,2
%A _Peter Luschny_, Apr 17 2014
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