A307979 Expansion of e.g.f. exp((cosh(x) - cos(x))/2) (even powers only).

1, 1, 3, 16, 133, 1576, 24783, 495496, 12245353, 364768576, 12838252443, 526095538816, 24781014246253, 1326767681420416, 80013978835916583, 5392682199766283776, 403287063337529642833, 33261775377836063850496, 3009257393136250807614003, 297176659119237977183973376

Offset: 0

Author

Ilya Gutkovskiy, May 08 2019

Keywords

• nonn

Comments

Number of partitions of a 2n-set into blocks congruent to 2 mod 4.

Crossrefs

Cf. A003724, A005046, A013469, A016825, A035457, A291975, A306347, A307978.

Programs

Mathematica

nmax = 19; Table[(CoefficientList[Series[Exp[(Cosh[x] - Cos[x])/2], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
a[n_] := a[n] = Sum[Boole[MemberQ[{2}, Mod[k, 4]]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[2 n], {n, 0, 19}]

Formula

a(n) = (2*n)! * [x^(2*n)] exp((cosh(x) - cos(x))/2).