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 A343665 Number of partitions of an n-set without blocks of size 5. 7
 1, 1, 2, 5, 15, 51, 197, 835, 3860, 19257, 102997, 586170, 3535645, 22496437, 150454918, 1054235150, 7718958995, 58905868192, 467530598983, 3851775136517, 32881385742460, 290387471713872, 2649226725182823, 24934118754400767, 241809265181914545, 2413608066257526577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..25. FORMULA E.g.f.: exp(exp(x) - 1 - x^5/5!). a(n) = n! * Sum_{k=0..floor(n/5)} (-1)^k * Bell(n-5*k) / ((n-5*k)! * k! * (5!)^k). MAPLE a:= proc(n) option remember; `if`(n=0, 1, add( `if`(j=5, 0, a(n-j)*binomial(n-1, j-1)), j=1..n)) end: seq(a(n), n=0..25); # Alois P. Heinz, Apr 25 2021 MATHEMATICA nmax = 25; CoefficientList[Series[Exp[Exp[x] - 1 - x^5/5!], {x, 0, nmax}], x] Range[0, nmax]! Table[n! Sum[(-1)^k BellB[n - 5 k]/((n - 5 k)! k! (5!)^k), {k, 0, Floor[n/5]}], {n, 0, 25}] a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 5, 0, Binomial[n - 1, k - 1] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}] CROSSREFS Cf. A000110, A000296, A027339, A097514, A124504, A343664, A343666, A343667, A343668, A343669. Sequence in context: A117426 A201168 A001681 * A192553 A053553 A276721 Adjacent sequences: A343662 A343663 A343664 * A343666 A343667 A343668 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 25 2021 STATUS approved

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Last modified May 26 01:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)