A001255 Squares of partition numbers.
1, 1, 4, 9, 25, 49, 121, 225, 484, 900, 1764, 3136, 5929, 10201, 18225, 30976, 53361, 88209, 148225, 240100, 393129, 627264, 1004004, 1575025, 2480625, 3833764, 5934096, 9060100, 13823524, 20839225, 31404816, 46812964, 69705801, 102880449, 151536100
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
Programs
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Haskell
a001255 = (^ 2) . a000041 -- Reinhard Zumkeller, Nov 15 2015
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Maple
seq(numbpart(k)^2, k=0..33); # Zerinvary Lajos, Jun 06 2007
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Mathematica
Table[ PartitionsP[n]^2, {n, 0, 33}] (* Ray Chandler, Nov 14 2005 *) -
PARI
a(n) = numbpart(n)^2; \\ Michel Marcus, May 01 2021
Formula
a(n) = A000041(n)^2.
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (48*n^2). - Vaclav Kotesovec, Dec 01 2015
Sum_{n>=1} 1/a(n) = A200089. - Amiram Eldar, May 01 2021
a(n) = [(x*y)^n] Product_{k>=1} 1 / ((1 - x^k) * (1 - y^k)). - Ilya Gutkovskiy, Apr 24 2025
Extensions
Extended by Ray Chandler, Nov 14 2005