A213359 Sum of all parts that are not the smallest part (counted with multiplicity) of all partitions of n.

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

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-François Alcover, Feb 21 2017, after Emeric Deutsch *)

Crossrefs

Cf. A066186, A092269, A092309, A268189.

Sequence in context: A275172 A281980 A137997 * A328000 A323006 A361257

Adjacent sequences: A213356 A213357 A213358 * A213360 A213361 A213362

Keyword

nonn

Author

Omar E. Pol, Jan 08 2013

Status

approved