%I A014968
%S A014968 0,1,2,4,7,12,20,32,50,77,116,172,252,364,520,736,1031,
%T A014968 1432,1974,2700,3668,4952,6644,8864,11764,15533,20412,26704,
%U A014968 34784,45124,58312,75072,96306,123128,156904,199320,252443
%N A014968 Expansion of (1/theta_4 - 1)/2.
%C A014968 Let p(n) = the number of partitions of n, p(i,n) = the number of parts 
               of the i-th partition of n, d(i,n) = the number of different parts 
               in the i-th partition of n. Then a(n) = Sum_{i=1}^{p(n)} Sum_{j=1}^d(i,
               n) binomial(d(i,n)-1,j-1). - Thomas Wieder (wieder.thomas(AT)t-online.de), 
               May 08 2005
%D A014968 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", 
               Springer-Verlag, p. 103.
%D A014968 A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring 
               at most thrice, in preparation.
%p A014968 A014968 := proc(n::integer) local a,i,j,prttn,prttnlst,ZahlTeile,ZahlVerschiedenerTeile; 
               #with(combinat); a := 0; prttnlst:=partition(n); for i from 1 to 
               nops(prttnlst) do prttn := prttnlst[i]; ZahlTeile := nops(prttn); 
               ZahlVerschiedenerTeile:=nops(convert(prttn,multiset)); for j from 
               1 to ZahlVerschiedenerTeile do a := a + binomial(ZahlVerschiedenerTeile-1,
               j-1); od; od; print("n, a(n): ",n, a); end proc; (Wieder)
%Y A014968 Equals (A015128(n)-1)/2.
%Y A014968 Sequence in context: A132218 A101230 A128129 this_sequence A126348 A006731 
               A000071
%Y A014968 Adjacent sequences: A014965 A014966 A014967 this_sequence A014969 A014970 
               A014971
%K A014968 nonn
%O A014968 0,3
%A A014968 N. J. A. Sloane (njas(AT)research.att.com).