OFFSET
0,8
COMMENTS
Number of partitions of n-set into blocks congruent to 1 mod 6.
FORMULA
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/6)} binomial(n-1,6*k) * a(n-6*k-1). - Seiichi Manyama, Sep 22 2023
MATHEMATICA
nmax = 30; CoefficientList[Series[Exp[Sum[x^(6 k + 1)/(6 k + 1)!, {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Boole[MemberQ[{1}, Mod[k, 6]]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Exp[x*HypergeometricPFQ[{}, {1/3, 1/2, 2/3, 5/6, 7/6}, x^6/46656]], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 15 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 08 2020
STATUS
approved