0,2

For n >= 1 a(n) is also the number of conjugacy classes in the automorphism group of the n-dimensional hypercube. This automorphism group is the wreath product of the cyclic group C_2 and the symmetric group S_n, its order is in sequence A000165. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Nov 04 2001

Euler transform of period 1 sequence [2,2,2,...].

A006330(n)+A001523(n)=a(n). - Michael Somos, Jul 22 2003

Also, number of noncongruent matrices in GL_n(Z): each Jordan block can only have +1 or -1 on the diagonal. - Michele Dondi (blazar(AT)lcm.mi.infn.it), Jun 15 2004

a(n) = Sum (k(1)+1)*(k(2)+1)*...*(k(n)+1), where the sum is taken over all (k(1),k(2),...,k(n)) such that k(1)+2*k(2)+...+n*k(n) = n, k(i)>=0, i=1..n, cf. A104510, A077285. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 21 2005

Convolution of partition numbers (A000041) with itself. - Graeme McRae (g_m(AT)mcraefamily.com), Jun 07 2006

Number of one-to-one partial endofunctions on n unlabeled points. Connected components are either cycles or "lines", hence two for each size. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 28 2006

Equals A000716: (1, 3, 9, 22, 561, 108,...) convolved with A010815. A000716 = the number of partitions of n into parts of 3 kinds = the Euler transform of [3,3,3,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2008]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

W. Y. C. Chen, K. Q. Ji and H. S. Wilf, BG-ranks and 2-cores, arXiv:math.CO/0605474.

H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 90.

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, 1999; see Proposition 2.5.2 on page 78.

T. D. Noe, Table of n, a(n) for n=0..500

E. R. Canfield, C. D. Savage and H. S. Wilf, Regularly spaced subsums of integer partitions

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 129

N. J. A. Sloane, Transforms

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

G.f.: Product 1/(1-x^m)^2; m=1..inf. a(n) = sum k=0, ..., n p(k)*p(n-k).

a(n) ~ 1/12*3^(1/4)*n^(-5/4)*exp(2/3*3^(1/2)*pi*n^(1/2)) - Joe Keane (jgk(AT)jgk.org), Sep 13 2002

G.f. : product(i=1, oo, (1+x^i)^(2*A001511(i))) (see A000041) - Jon Perry (perry(AT)globalnet.co.uk), Jun 06 2004

with(combinat): A000712:=n->sum(numbpart(k)*numbpart(n-k), k=0..n): seq(A000712(n), n=0..37); (E. Deutsch)

CoefficientList[ Series[ Product[1/(1 - x^n)^2, {n, 40}], {x, 0, 37}], x] (from Robert G. Wilson v Feb 03 2005)

(PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(1/eta(X)^2, n))

Cf. A000165, A000041, A002107 (reciprocal of g.f.).

Cf. A002720.

A000716, A010815 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2008]

Sequence in context: A103928 A103929 A121597 this_sequence A032442 A102688 A001629

Adjacent sequences: A000709 A000710 A000711 this_sequence A000713 A000714 A000715

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Joe Keane (jgk(AT)jgk.org), Nov 17 2001

More terms from Michele Dondi (blazar(AT)lcm.mi.infn.it), Jun 15 2004