This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279172 #12 Feb 16 2025 08:33:37
%S A279172 0,1,1,-1,-3,3,17,-17,-155,155,2073,-2073,-38227,38227,929569,-929569,
%T A279172 -28820619,28820619,1109652905,-1109652905,-51943281731,51943281731,
%U A279172 2905151042481,-2905151042481,-191329672483963,191329672483963,14655626154768697,-14655626154768697
%N A279172 The autosequence of the first kind between A226158(n) and A278331(n).
%C A279172 Peter Luschny introduced the extended Genocchi numbers A226158(n), an autosequence of the first kind. They are linked to the second Bernoulli numbers B+(n) = A164555(n)/A027642(n). Here + is an exponent.
%C A279172 This yields the possible Genocchi twin numbers: -1, -1 followed by a(n).
%H A279172 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/GenocchiNumber.html">Genocchi Number</a>
%H A279172 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%H A279172 Wikipedia, <a href="http://en.wikipedia.org/wiki/Genocchi_number">Genocchi number</a>
%F A279172 a(n) = A226158(n+2) - A226158(n+1).
%F A279172 a(n) = 2*(2^(n+1) -1)*B+(n+1) -2*(2^(n+2) -1)*B+(n+2).
%t A279172 a[n_] := (n+2)*EulerE[n+1, 0] - (n+1)*EulerE[n, 0]; a[0] = 0; Table[a[n], {n, 0, 30}] (* or: *)
%t A279172 Join[{0}, Array[#*EulerE[#-1, 0]&, 32] // Differences // Rest]
%Y A279172 Cf. A000918, A027642, A036968, A051716, A164555, A226158, A278331.
%K A279172 sign
%O A279172 0,5
%A A279172 _Jean-François Alcover_ and _Paul Curtz_, Dec 07 2016