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 A333882 Expansion of e.g.f. exp(Sum_{k>=0} x^(5*k + 1) / (5*k + 1)!). 4
 1, 1, 1, 1, 1, 1, 2, 8, 29, 85, 211, 464, 1399, 7801, 45410, 216581, 853218, 2896002, 11708734, 79817500, 615700986, 4012571831, 21538473686, 98707812691, 501634082800, 3983368886226, 37404203343457, 305886831698593, 2069143637726674, 11924094649669375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Number of partitions of n-set into blocks congruent to 1 mod 5. LINKS Table of n, a(n) for n=0..29. FORMULA a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/5)} binomial(n-1,5*k) * a(n-5*k-1). - Seiichi Manyama, Sep 22 2023 MATHEMATICA nmax = 29; CoefficientList[Series[Exp[Sum[x^(5 k + 1)/(5 k + 1)!, {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! a[n_] := a[n] = Sum[Boole[MemberQ[{1}, Mod[k, 5]]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 29}] nmax = 30; CoefficientList[Series[Exp[x*HypergeometricPFQ[{}, {2/5, 3/5, 4/5, 6/5}, x^5/3125]], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 15 2020 *) CROSSREFS Cf. A000110, A003724, A306347, A333881, A333883. Sequence in context: A364523 A107025 A212385 * A365760 A365758 A365759 Adjacent sequences: A333879 A333880 A333881 * A333883 A333884 A333885 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 08 2020 STATUS approved

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Last modified February 26 07:39 EST 2024. Contains 370335 sequences. (Running on oeis4.)