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A092265 Sum of smallest parts of all partitions of n into distinct parts. 8
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-Fran├žois Alcover, Jan 21 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A046746, A005895, A006128, A092319, A092316, A034296, A237665.

Cf. A026832.

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 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)