cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A001255 Squares of partition numbers.

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%I A001255 #37 Apr 24 2025 06:29:19
%S A001255 1,1,4,9,25,49,121,225,484,900,1764,3136,5929,10201,18225,30976,53361,
%T A001255 88209,148225,240100,393129,627264,1004004,1575025,2480625,3833764,
%U A001255 5934096,9060100,13823524,20839225,31404816,46812964,69705801,102880449,151536100
%N A001255 Squares of partition numbers.
%H A001255 T. D. Noe, <a href="/A001255/b001255.txt">Table of n, a(n) for n = 0..1000</a>
%F A001255 a(n) = A000041(n)^2.
%F A001255 a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (48*n^2). - _Vaclav Kotesovec_, Dec 01 2015
%F A001255 Sum_{n>=1} 1/a(n) = A200089. - _Amiram Eldar_, May 01 2021
%F A001255 a(n) = A006907(n) + A051748(n) + A051749(n). - _R. J. Mathar_, Mar 09 2022
%F A001255 a(n) = [(x*y)^n] Product_{k>=1} 1 / ((1 - x^k) * (1 - y^k)). - _Ilya Gutkovskiy_, Apr 24 2025
%p A001255 seq(numbpart(k)^2, k=0..33); # _Zerinvary Lajos_, Jun 06 2007
%t A001255 Table[ PartitionsP[n]^2, {n, 0, 33}] (* _Ray Chandler_, Nov 14 2005 *)
%o A001255 (Haskell)
%o A001255 a001255 = (^ 2) . a000041  -- _Reinhard Zumkeller_, Nov 15 2015
%o A001255 (PARI) a(n) = numbpart(n)^2; \\ _Michel Marcus_, May 01 2021
%Y A001255 Cf. A000041, A000290, A304990, A200089.
%Y A001255 Cf. A133042, A054440.
%K A001255 nonn,easy
%O A001255 0,3
%A A001255 _N. J. A. Sloane_
%E A001255 Extended by _Ray Chandler_, Nov 14 2005