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

0,3

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

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) = A006907(n) + A051748(n) + A051749(n). - R. J. Mathar, Mar 09 2022

Maple

seq(numbpart(k)^2, k=0..33); # Zerinvary Lajos, Jun 06 2007

Mathematica

Table[ PartitionsP[n]^2, {n, 0, 33}] (* Ray Chandler, Nov 14 2005 *)

Prog

(Haskell)
a001255 = (^ 2) . a000041  -- Reinhard Zumkeller, Nov 15 2015
(PARI) a(n) = numbpart(n)^2; \\ Michel Marcus, May 01 2021

Crossrefs

Cf. A000041, A000290, A304990, A200089.

Cf. A133042, A054440.

Sequence in context: A158182 A158183 A158184 * A357754 A133019 A376746

Adjacent sequences: A001252 A001253 A001254 * A001256 A001257 A001258

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Extended by Ray Chandler, Nov 14 2005

Status

approved