A307979 - OEIS

%I #7 May 08 2019 22:18:28

%S 1,1,3,16,133,1576,24783,495496,12245353,364768576,12838252443,

%T 526095538816,24781014246253,1326767681420416,80013978835916583,

%U 5392682199766283776,403287063337529642833,33261775377836063850496,3009257393136250807614003,297176659119237977183973376

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

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

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

%t 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}]

%t 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}]

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 08 2019