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a(0)=1; thereafter a(n) = 2*A110501(n+1) - A005439(n).
1

%I #11 Apr 14 2023 13:06:46

%S 1,1,4,26,254,3538,67014,1660866,52230550,2033261906,96018823814,

%T 5409008246626,358368831222006,27589872391918194,2442595357421865574,

%U 246430234111929035906,28106918525950072081622,3598669462582938225587602,513978991104098010878849094

%N a(0)=1; thereafter a(n) = 2*A110501(n+1) - A005439(n).

%H Bishal Deb and Alan D. Sokal, <a href="https://arxiv.org/abs/2212.07232">Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers</a>, arXiv:2212.07232 [math.CO], 2022. Section 3.1.

%o (Python)

%o from math import comb

%o from sympy import bernoulli

%o def A362112(n): return ((4<<(m:=n+1<<1))-4)*abs(bernoulli(m))-abs(sum(comb(n,k)*(2-(2<<n+k+1))*bernoulli(n+k+1) for k in range(n+1))) # _Chai Wah Wu_, Apr 14 2023

%Y Cf. A110501, A005439.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 14 2023

%E More terms from _Chai Wah Wu_, Apr 14 2023