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A306347
Expansion of e.g.f. exp((sin(x) + sinh(x))/2).
8
1, 1, 1, 1, 1, 2, 7, 22, 57, 128, 389, 1904, 9329, 38040, 132147, 542648, 3283633, 20997824, 114657097, 536178880, 2784500161, 19876061312, 153326461311, 1034551839872, 6051063485481, 38079448046208, 312420426154893, 2785055242928768, 22141255520251313
OFFSET
0,6
COMMENTS
Number of partitions of n-set into blocks congruent to 1 mod 4.
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * a(n-4*k-1). - Seiichi Manyama, Mar 17 2022
MATHEMATICA
nmax = 28; CoefficientList[Series[Exp[(Sin[x] + Sinh[x])/2], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Boole[MemberQ[{1}, Mod[k, 4]]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 28}]
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp((sin(x)+sinh(x))/2))) \\ Seiichi Manyama, Mar 17 2022
(PARI) a(n) = if(n==0, 1, sum(k=0, (n-1)\4, binomial(n-1, 4*k)*a(n-4*k-1))); \\ Seiichi Manyama, Mar 17 2022
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 08 2019
STATUS
approved