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 A096770 a(1) = 1; for n >= 1, replace each part, with repetitions, of every part k in each partition of n with a(k), then take the sum to get a(n+1). 0
 1, 1, 3, 8, 21, 51, 127, 303, 734, 1751, 4200, 10004, 23918, 56981, 135958, 323996, 772530, 1840993, 4388456, 10458354, 24926754, 59405383, 141581236, 337417607, 804153140, 1916469872, 4567399008, 10885108498, 25941679513, 61824709789 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Comment from Michael Taktikos, Sep 04 2004: The following is a much simpler definition of this sequence: a[1] = 1; a[n_] := Mod[Sum[a[k], {k, 1, n - 1}], n - 1] LINKS FORMULA a(n+1) = sum{k=1 to n} (sum{j|k} a(j)) * p(n-k), where p(k) is the number of partitions of k (A000041). EXAMPLE We have the partitions of 4: 1+1+1+1, 1+1+2, 1+3, 2+2, 4; replace and add: 1+1+1+1 +1+1+1 +1+3 +1+1 +8 = 21 = a(5). MATHEMATICA a[1] = 1; a[n_] := a[n] = Block[{j, k, s = 0}, For[k = 1, k < n, k++, j = Divisors[k]; s = s + Plus @@ ((a /@ j)PartitionsP[n - k - 1])]; s]; Table[ a[n], {n, 30}] (* Robert G. Wilson v, Aug 25 2004 *) (* or slower *) (* first *) Needs["DiscreteMath`Combinatorica`"] (* then *) a[1] = 1; a[n_] := a[n] = Block[{p = Sort[ Flatten[ Partitions[n - 1]] ]}, Plus @@ (a /@ p)]; Table[ a[n], {n, 30}] (* Robert G. Wilson v, Aug 25 2004 *) CROSSREFS Sequence in context: A238831 A322059 A259714 * A007835 A152086 A014396 Adjacent sequences:  A096767 A096768 A096769 * A096771 A096772 A096773 KEYWORD nonn,easy AUTHOR Leroy Quet, Aug 17 2004 EXTENSIONS More terms from Robert G. Wilson v, Aug 25 2004 STATUS approved

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Last modified September 20 10:10 EDT 2019. Contains 327229 sequences. (Running on oeis4.)