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A318156 Expansion of (1/(1 - x)) * Sum_{k>=1} x^(k*(2*k-1)) / Product_{j=1..2*k-1} (1 - x^j). 1
0, 1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 27, 35, 44, 55, 69, 85, 104, 127, 154, 186, 224, 268, 320, 381, 452, 534, 630, 741, 869, 1017, 1187, 1382, 1606, 1862, 2155, 2489, 2869, 3301, 3792, 4349, 4979, 5692, 6497, 7405, 8429, 9581, 10876, 12331, 13963, 15792, 17840, 20131, 22691 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of A067659.

LINKS

Table of n, a(n) for n=0..53.

Joerg Arndt, Matters Computational (The Fxtbook), section 16.4.2 "Partitions into distinct parts", page 350.

Index entries for sequences related to partitions

FORMULA

a(n) = A036469(n) - A318155(n).

a(n) = A318155(n) - A078616(n).

a(n) ~ exp(Pi*sqrt(n/3)) * 3^(1/4) / (4*Pi*n^(1/4)). - Vaclav Kotesovec, Aug 20 2018

MAPLE

b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2, 0,

      `if`(n=0, t, add(b(n-i*j, i-1, abs(t-j)), j=0..min(n/i, 1))))

    end:

a:= proc(n) option remember; b(n$2, 0)+`if`(n>0, a(n-1), 0) end:

seq(a(n), n=0..60);

MATHEMATICA

nmax = 53; CoefficientList[Series[1/(1 - x) Sum[x^(k (2 k - 1))/Product[(1 - x^j), {j, 1, 2 k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 53; CoefficientList[Series[(QPochhammer[-x, x] - QPochhammer[x])/(2 (1 - x)), {x, 0, nmax}], x]

CROSSREFS

Cf. A036469, A067659, A078616, A306145, A318155.

Sequence in context: A272691 A192433 A189083 * A272948 A164001 A117598

Adjacent sequences:  A318153 A318154 A318155 * A318157 A318158 A318159

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 19 2018

STATUS

approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)