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A072213 Number of partitions of n^2. 25

%I #19 Dec 07 2019 12:18:23

%S 1,1,5,30,231,1958,17977,173525,1741630,18004327,190569292,2056148051,

%T 22540654445,250438925115,2814570987591,31946390696157,

%U 365749566870782,4219388528587095,49005643635237875,572612058898037559

%N Number of partitions of n^2.

%H Alois P. Heinz, <a href="/A072213/b072213.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = A000041(n^2).

%F a(n) ~ exp(Pi*sqrt(2/3)*n) / (4*sqrt(3)*n^2). - _Vaclav Kotesovec_, Dec 01 2015

%p A072213 := proc(n) combinat[numbpart](n^2) ; end proc:

%p seq(A072213(n),n=0..10) ; # _R. J. Mathar_, Jan 24 2011

%t Table[ PartitionsP[n^2], {n, 1, 20}]

%o (PARI) a(n)=numbpart(n^2)

%o (PARI) a(n)=polcoeff(1/eta(x),n^2,x)

%o (Sage) [number_of_partitions(n^2)for n in range(0,26)] # _Zerinvary Lajos_, Nov 26 2009

%Y Cf. A000041, A000290, A072243.

%Y Cf. A161407, A161408. - _Reinhard Zumkeller_, Jun 10 2009

%K nonn

%O 0,3

%A _Jeff Burch_, Jul 03 2002

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Last modified April 18 20:26 EDT 2024. Contains 371781 sequences. (Running on oeis4.)