%I A077045
%S A077045 1,1,2,7,44,381,4332,60691,1012664,19610233,432457640,10701243741,
%T A077045 293661065788,8851373201919,290711372717976,10334165623697259,
%U A077045 395320344293410544,16192709833199300337,707125993042984343136
%N A077045 Doubly restricted composition numbers: number of compositions of 1+2+3+...+n=n(n+1)/
               2 into exactly n positive integers each no more than n.
%H A077045 <a href="Sindx_Com.html#comp">Index entries for sequences related to 
               compositions</a>
%F A077045 a(n) =A077042(n, n). Roughly n^(n-3/2)*sqrt(6/pi) by the central limit 
               theorem and something like n^n*sqrt(6/(pi*(n^3+0.3*n^2-0.91*n+0.3)) 
               seems to be even closer.
%e A077045 a(3)=7 since the compositions of 1+2+3=6 into exactly 3 positive integers 
               each no more than 3 are: 1+2+3, 1+3+2, 2+1+3, 2+2+2, 2+3+1, 3+1+2, 
               3+2+1.
%Y A077045 Cf. A077042, A077046, A077047, A077048.
%Y A077045 Sequence in context: A145073 A111561 A000155 this_sequence A128579 A001046 
               A158257
%Y A077045 Adjacent sequences: A077042 A077043 A077044 this_sequence A077046 A077047 
               A077048
%K A077045 nice,nonn
%O A077045 0,3
%A A077045 Henry Bottomley (se16(AT)btinternet.com), Oct 22 2002