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 A092265 Sum of smallest parts of all partitions of n into distinct parts. 10
 1, 2, 4, 5, 8, 10, 14, 16, 23, 26, 34, 40, 50, 58, 74, 83, 102, 120, 142, 164, 198, 226, 266, 308, 359, 412, 482, 548, 634, 730, 834, 950, 1094, 1240, 1416, 1609, 1826, 2068, 2350, 2648, 2994, 3382, 3806, 4280, 4826, 5408, 6070, 6806, 7619, 8522, 9534, 10632 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA G.f.: sum(n>=1, -1 + prod(k>=n, 1+x^k ) ). G.f.: sum(n>=1, n*x^n*prod(k>=n+1,1+x^k)) - Joerg Arndt, Jan 29 2011 G.f.: sum(k>=1, x^(k*(k+1)/2)/(1-x^k)/prod(i=1..k, 1-x^i ) ). - Vladeta Jovovic, Aug 10 2004 Conjecture: a(n) = A034296(n) + A237665(n+1). - George Beck, May 06 2017 a(n) ~ exp(Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 20 2018 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1,      `if`(i>n, 0, b(n, i+1)+b(n-i, i+1)))     end: a:= n-> add(j*b(n-j, j+1), j=1..n): seq(a(n), n=1..80);  # Alois P. Heinz, Feb 03 2016 MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i + 1] + b[n - i, i + 1]]]; a[n_] := Sum[j*b[n - j, j + 1], {j, 1, n}]; Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Jan 21 2017, after Alois P. Heinz *) CROSSREFS Cf. A046746, A005895, A006128, A092319, A092316, A034296, A237665. Cf. A026832, A336902, A336903. Sequence in context: A067941 A259711 A182195 * A262937 A249508 A163295 Adjacent sequences:  A092262 A092263 A092264 * A092266 A092267 A092268 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Feb 14 2004 EXTENSIONS More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004 STATUS approved

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Last modified August 1 13:51 EDT 2021. Contains 346391 sequences. (Running on oeis4.)