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A213359 Sum of all parts that are not the smallest part (counted with multiplicity) of all partitions of n. 2
0, 0, 2, 5, 16, 27, 59, 96, 164, 260, 415, 606, 923, 1336, 1911, 2698, 3787, 5203, 7142, 9646, 12962, 17295, 22902, 30063, 39315, 51104, 66013, 84898, 108658, 138397, 175593, 221872, 279207, 350248, 437607, 545093, 676764, 837873, 1033961, 1272730, 1562137 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A066186(n) - A092309(n).

G.f.: Sum_{i>0}(x^i/(1-x^i))(Sum_{j>i}(j*x^j/(1-x^j))/Product_{j>i}(1-x^j)) (obtained by logarithmic differentiation of the bivariate g.f. given in A268189). - Emeric Deutsch, Feb 02 2016

EXAMPLE

a(4) = 5 because the partitions of 4 are [1,1,1,1], [1,1,2], [1,3], [2,2], and [4], having sum of parts that are not the smallest 0, 2, 3, 0, and 0, respectively, and 0 + 2 + 3 + 0 + 0 = 5. - Emeric Deutsch, Feb 02 2016

MAPLE

g := add(x^i*add(j*x^j/(1-x^j), j = i+1 .. 80)/((1-x^i)*mul(1-x^j, j = i+1 .. 80)), i = 1 .. 80): gser := series(g, x = 0, 55): seq(coeff(gser, x, n), n = 1 .. 40); # Emeric Deutsch, Feb 02 2016

MATHEMATICA

max = 42; gser = Sum[x^i*Sum[j*x^j/(1-x^j), {j, i+1, max}]/((1-x^i)* Product[1-x^j, {j, i+1, max}]), {i, 1, max}]+O[x]^max; CoefficientList[ gser, x] // Rest (* Jean-Fran├žois Alcover, Feb 21 2017, after Emeric Deutsch *)

CROSSREFS

Cf. A066186, A092269, A092309, A268189.

Sequence in context: A275172 A281980 A137997 * A328000 A323006 A139022

Adjacent sequences:  A213356 A213357 A213358 * A213360 A213361 A213362

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jan 08 2013

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)