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%I #17 Mar 17 2022 11:42:22
%S 1,0,0,1,0,0,10,1,0,280,120,1,15400,17160,2080,1401401,3203200,
%T 1290640,190623040,775975201,712150400,36321556720,239000886400,
%U 413465452401,9339501072000,91625659447400,266045692290560,3216459513124001,42923384190336000,193108117771690680
%N Expansion of e.g.f. exp((sinh(x) - sin(x))/2).
%C Number of partitions of n-set into blocks congruent to 3 mod 4.
%H Seiichi Manyama, <a href="/A307978/b307978.txt">Table of n, a(n) for n = 0..608</a>
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/4)} binomial(n-1,4*k+2) * a(n-4*k-3). - _Seiichi Manyama_, Mar 17 2022
%t nmax = 29; CoefficientList[Series[Exp[(Sinh[x] - Sin[x])/2], {x, 0, nmax}], x] Range[0, nmax]!
%t a[n_] := a[n] = Sum[Boole[MemberQ[{3}, Mod[k, 4]]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 29}]
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp((sinh(x)-sin(x))/2))) \\ _Seiichi Manyama_, Mar 17 2022
%o (PARI) a(n) = if(n==0, 1, sum(k=0, (n-3)\4, binomial(n-1, 4*k+2)*a(n-4*k-3))); \\ _Seiichi Manyama_, Mar 17 2022
%Y Cf. A002017, A003724, A004767, A005046, A013369, A035462, A291975, A306347, A307979.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, May 08 2019
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