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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316231 Expansion of Product_{k>=1} 1/(1 + q(k)*x^k), where q(k) = number of partitions of k into distinct parts (A000009). 1
1, -1, 0, -2, 1, -2, 3, -3, 6, -8, 14, -10, 28, -26, 41, -73, 90, -112, 155, -221, 288, -501, 560, -799, 1153, -1610, 1953, -3095, 4073, -5224, 7295, -9536, 13536, -18402, 24757, -32936, 48714, -60790, 82101, -113247, 153330, -201522, 275713, -367041, 492991 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..44.

Eric Weisstein's World of Mathematics, Partition Function Q

Index entries for sequences related to partitions

FORMULA

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*q(j)^k*x^(j*k)/k).

MATHEMATICA

nmax = 44; CoefficientList[Series[Product[1/(1 + PartitionsQ[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 44; CoefficientList[Series[Exp[Sum[Sum[(-1)^k PartitionsQ[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (-PartitionsQ[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 44}]

CROSSREFS

Cf. A000009, A089254, A270995, A279785, A304786, A316230.

Sequence in context: A109266 A022876 A242692 * A014781 A214500 A066016

Adjacent sequences:  A316228 A316229 A316230 * A316232 A316233 A316234

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 27 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 January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)