A072213 Number of partitions of n^2.

1, 1, 5, 30, 231, 1958, 17977, 173525, 1741630, 18004327, 190569292, 2056148051, 22540654445, 250438925115, 2814570987591, 31946390696157, 365749566870782, 4219388528587095, 49005643635237875, 572612058898037559

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..900 (terms 0..250 from Alois P. Heinz)

Formula

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

a(n) ~ exp(Pi*sqrt(2/3)*n) / (4*sqrt(3)*n^2). - Vaclav Kotesovec, Dec 01 2015

Maple

A072213 := proc(n) combinat[numbpart](n^2) ; end proc:
seq(A072213(n), n=0..10) ; # R. J. Mathar, Jan 24 2011

Mathematica

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

Prog

(PARI) a(n)=numbpart(n^2)
(PARI) a(n)=polcoeff(1/eta(x), n^2, x)
(Sage) [number_of_partitions(n^2)for n in range(0, 26)] # Zerinvary Lajos, Nov 26 2009

Crossrefs

Cf. A000041, A000290, A072243, A219430.

Cf. A161407, A161408. - Reinhard Zumkeller, Jun 10 2009

Sequence in context: A345190 A144498 A201368 * A257741 A308946 A346681

Adjacent sequences: A072210 A072211 A072212 * A072214 A072215 A072216

Keyword

nonn

Author

Jeff Burch, Jul 03 2002

Status

approved