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 A307978 Expansion of e.g.f. exp((sinh(x) - sin(x))/2). 6
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)