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 A138135 Number of parts > 1 in the last section of the set of partitions of n. 25
 0, 1, 1, 3, 3, 8, 8, 17, 20, 34, 41, 68, 80, 123, 153, 219, 271, 382, 469, 642, 795, 1055, 1305, 1713, 2102, 2713, 3336, 4241, 5190, 6545, 7968, 9950, 12090, 14953, 18104, 22255, 26821, 32752, 39371, 47774, 57220, 69104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Also first differences of A096541. For more information see A135010. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A096541(n)-A096541(n-1) = A138137(n)-A000041(n-1) = A006128(n)-A006128(n-1)-A000041(n-1). a(n) ~ exp(Pi*sqrt(2*n/3))*(2*gamma - 2 + log(6*n/Pi^2))/(8*sqrt(3)*n), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 24 2016 MAPLE b:= proc(n, i) option remember; local f, g;       if n=0 or i=1 then [1, 0]     else f:= b(n, i-1); g:= `if`(i>n, [0, 0], b(n-i, i));          [f[1]+g[1], f[2]+g[2]+`if`(i>1, g[1], 0)]       fi     end: a:= n-> b(n, n)[2]-b(n-1, n-1)[2]: seq (a(n), n=1..60); # Alois P. Heinz, Apr 04 2012 MATHEMATICA a[n_] := DivisorSigma[0, n] - 1 + Sum[(DivisorSigma[0, k] - 1)*(PartitionsP[n - k] - PartitionsP[n - k - 1]), {k, 1, n - 1}]; Table[a[n], {n, 1, 42}] (* Jean-François Alcover, Jan 14 2013, from 1st formula *) Table[Length@Flatten@Select[IntegerPartitions[n], FreeQ[#, 1] &], {n, 1, 42}]  (* Robert Price, May 01 2020 *) PROG (PARI) a(n)=numdiv(n)-1+sum(k=1, n-1, (numdiv(k)-1)*(numbpart(n-k) - numbpart(n-k-1))) \\ Charles R Greathouse IV, Jan 14 2013 CROSSREFS Zero together with the column k=2 of A207031. Cf. A000041, A006128, A096541, A135010, A138121, A138137. Sequence in context: A058617 A205977 A238623 * A113166 A126872 A094966 Adjacent sequences:  A138132 A138133 A138134 * A138136 A138137 A138138 KEYWORD nonn AUTHOR Omar E. Pol, Mar 30 2008 STATUS approved

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Last modified June 1 12:49 EDT 2020. Contains 334762 sequences. (Running on oeis4.)