0,5

Also sum of the sizes of the Durfee squares of all self-conjugate partitions of n. Example: a(13)=7 because there are three self-conjugate partitions of 13, namely [7,1,1,1,1,1,1], [5,3,3,1,1] and [4,4,3,2], having Durfee squares of sizes 1,3 and 3, respectively. a(n)=sum(k*A116422(n,k),k=1..floor(sqrt(n))). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 14 2006

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (pp. 27-28).

G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004 (pp. 75-78).

A. Knopfmacher and N. Robbins, Identities for the total number of parts in partitions of integers, Util. Math. 67 (2005), 9-18.

G.f.: sum x^(2k-1)/(1+x^(2k-1); k=1..inf * prod (1+x^(2m-1); m=1..inf

Sum_{k>0} (k*x^(k^2)/Product_{j=1..k} (1-x^(2*j))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2004

G.f.=sum(kx^(k^2)/product(1-x^(2i),i =1..k),k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 14 2006

a(13)=7 because the partitions of 13 into distinct odd parts are [13], [9,3,1] and [7,5,1] and we have 1+3+3=7 parts.

g:=sum(k*x^(k^2)/product(1-x^(2*i), i =1..k), k=1..20):gser:=series(g, x=0, 52): seq(coeff(gser, x, n), n=0..50); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 14 2006

Cf. A015723, A000700, A067619, A006128.

Cf. A032021.

Cf. A116422.

Sequence in context: A157333 A002852 A099875 this_sequence A166235 A143591 A085063

Adjacent sequences: A079496 A079497 A079498 this_sequence A079500 A079501 A079502

nonn

Arnold Knopfmacher (arnoldk(AT)cam.wits.ac.za), Jan 21 2003