A240560 a(n) = 2^n*E(n,1/2) + 2^(n+1)*E(n+1,0), where E(n,x) the Euler polynomials.
0, 0, 1, 0, -11, 0, 211, 0, -6551, 0, 303271, 0, -19665491, 0, 1704396331, 0, -190473830831, 0, 26684005437391, 0, -4581126864886571, 0, 946075012113714451, 0, -231406946026650896711, 0, 66164529094650835995511, 0, -21866924546405967976005251
Offset: 0
Keywords
Programs
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Maple
A240560 := n -> euler(n) + 2^(n+1)*euler(n+1, 0): seq(A240560(n), n=0..28);
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Mathematica
skp[n_, x_] := Sum[Binomial[n, k]*EulerE[k]*If[n==k, 1, x^(n-k)], {k, 0, n}]; a[n_] := skp[n, 0] + skp[n+1, -1]; Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Jul 08 2019 *)