login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A369887 Sum of products of squares of parts , counted without multiplicity, in all partitions of n. 1
1, 1, 5, 14, 34, 95, 208, 537, 1090, 2812, 5566, 12480, 26199, 53486, 112866, 229111, 450800, 885030, 1778190, 3319846, 6624376, 12354288, 23674929, 43485580, 81441398, 149864634, 273431081, 503205344, 906757150, 1630802024, 2920280596, 5166820832 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{k>=1} 1 + k^2*x^k/(1-x^k).
EXAMPLE
The partitions of 4 are 4, 3+1, 2+2, 2+1+1, 1+1+1+1. So a(4) = 16 + 9 + 4 + 4 + 1 = 34.
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^2*x^k/(1-x^k)))
CROSSREFS
Cf. A077335.
Sequence in context: A094584 A023515 A047860 * A083332 A101015 A076858
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 04 2024
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 07:43 EDT 2024. Contains 371799 sequences. (Running on oeis4.)