login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A318155 Expansion of (1/(1 - x)) * Sum_{k>=0} x^(k*(2*k+1)) / Product_{j=1..2*k} (1 - x^j). 1
1, 1, 1, 2, 3, 5, 7, 10, 13, 17, 22, 28, 35, 44, 55, 68, 84, 103, 126, 153, 185, 223, 268, 320, 381, 452, 535, 631, 742, 870, 1018, 1188, 1383, 1607, 1863, 2155, 2489, 2869, 3301, 3792, 4348, 4978, 5691, 6496, 7404, 8428, 9580, 10875, 12330, 13962, 15791, 17840, 20131, 22691 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Partial sums of A067661.

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) - A318156(n).

a(n) = A318156(n) + A078616(n).

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

MAPLE

a:=series((1/(1-x))*add(x^(k*(2*k+1))/mul((1-x^j), j=1..2*k), k=0..100), x=0, 54): seq(coeff(a, x, n), n=0..53); # Paolo P. Lava, Apr 02 2019

MATHEMATICA

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

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

CROSSREFS

Cf. A036469, A067661, A078616, A304620, A318156.

Sequence in context: A253170 A337567 A177332 * A282569 A213213 A319470

Adjacent sequences:  A318152 A318153 A318154 * A318156 A318157 A318158

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 19 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 1 03:36 EDT 2020. Contains 337441 sequences. (Running on oeis4.)