A307978 Expansion of e.g.f. exp((sinh(x) - sin(x))/2).

1, 0, 0, 1, 0, 0, 10, 1, 0, 280, 120, 1, 15400, 17160, 2080, 1401401, 3203200, 1290640, 190623040, 775975201, 712150400, 36321556720, 239000886400, 413465452401, 9339501072000, 91625659447400, 266045692290560, 3216459513124001, 42923384190336000, 193108117771690680

Offset

0,7

Comments

Number of partitions of n-set into blocks congruent to 3 mod 4.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..608

Formula

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

Mathematica

nmax = 29; CoefficientList[Series[Exp[(Sinh[x] - Sin[x])/2], {x, 0, nmax}], x] Range[0, nmax]!
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}]

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp((sinh(x)-sin(x))/2))) \\ Seiichi Manyama, Mar 17 2022
(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

Crossrefs

Cf. A002017, A003724, A004767, A005046, A013369, A035462, A291975, A306347, A307979.

Sequence in context: A265373 A309202 A105031 * A367614 A367616 A118762

Adjacent sequences: A307975 A307976 A307977 * A307979 A307980 A307981

Keyword

nonn

Author

Ilya Gutkovskiy, May 08 2019

Status

approved