A279172 The autosequence of the first kind between A226158(n) and A278331(n).

0, 1, 1, -1, -3, 3, 17, -17, -155, 155, 2073, -2073, -38227, 38227, 929569, -929569, -28820619, 28820619, 1109652905, -1109652905, -51943281731, 51943281731, 2905151042481, -2905151042481, -191329672483963, 191329672483963, 14655626154768697, -14655626154768697

Offset: 0

Author

Jean-François Alcover and Paul Curtz, Dec 07 2016

Keywords

• sign

Comments

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.

This yields the possible Genocchi twin numbers: -1, -1 followed by a(n).

Links

• Eric Weisstein's MathWorld, Genocchi Number
• OEIS Wiki, Autosequence
• Wikipedia, Genocchi number

Crossrefs

Cf. A000918, A027642, A036968, A051716, A164555, A226158, A278331.

Programs

Mathematica

a[n_] := (n+2)*EulerE[n+1, 0] - (n+1)*EulerE[n, 0]; a[0] = 0; Table[a[n], {n, 0, 30}] (* or: *)
Join[{0}, Array[#*EulerE[#-1, 0]&, 32] // Differences // Rest]

Formula

a(n) = A226158(n+2) - A226158(n+1).

a(n) = 2*(2^(n+1) -1)*B+(n+1) -2*(2^(n+2) -1)*B+(n+2).