%I A104382
%S A104382 1,1,1,1,2,1,1,4,4,1,1,7,12,6,1,1,10,27,27,10,1,1,13,52,84,57,14,1,1,17,
%T A104382 91,206,221,110,21,1,1,22,147,441,674,532,201,29,1,1,27,225,864,1747,
%U A104382 1945,1175,352,41,1,1,32,331,1575,4033,5942,5102,2462,598,55,1,1,38,469
%N A104382 Triangle, read by rows, where T(n,k) equals number of distinct partitions 
               of triangular number n*(n+1)/2 into k different summands for n>=k>
               =1.
%C A104382 Secondary diagonal equals partitions of n - 1 (A000065). Third diagonal 
               is A104384. Third column is A104385. Row sums are A104383 where limit_{n 
               --> inf} A104383(n+1)/A104383(n) = exp(sqrt(Pi^2/6)) = 3.605822247984...
%D A104382 Abramowitz, M. and Stegun, I. A. (Eds.). "Partitions into Distinct Parts." 
               S24.2.2 in Handbook of Mathematical Functions with Formulas, Graphs 
               and Mathematical Tables, 9th printing. New York: Dover, pp. 825-826, 
               1972.
%H A104382 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A104382 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PartitionFunctionQ.html">Partition Function Q.</a>
%F A104382 T(n, 1)=T(n, n)=1, T(n, n-1)=A000065(n-1), T(n, 2)=[(n*(n+1)/2-1)/2].
%e A104382 Rows begin:
%e A104382 1;
%e A104382 1,1;
%e A104382 1,2,1;
%e A104382 1,4,4,1;
%e A104382 1,7,12,6,1;
%e A104382 1,10,27,27,10,1;
%e A104382 1,13,52,84,57,14,1;
%e A104382 1,17,91,206,221,110,21,1;
%e A104382 1,22,147,441,674,532,201,29,1;
%e A104382 1,27,225,864,1747,1945,1175,352,41,1;
%e A104382 1,32,331,1575,4033,5942,5102,2462,598,55,1; ...
%o A104382 (PARI) {T(n,k)=if(n<k|k<1,0,polcoeff(polcoeff( prod(i=1,n*(n+1)/2,1+y*x^i,
               1+x*O(x^(n*(n+1)/2))),n*(n+1)/2,x),k,y))}
%Y A104382 Cf. A008289, A000009, A000065, A104383, A104384, A104385.
%Y A104382 Sequence in context: A034368 A113582 A118245 this_sequence A086629 A156184 
               A126770
%Y A104382 Adjacent sequences: A104379 A104380 A104381 this_sequence A104383 A104384 
               A104385
%K A104382 nonn,tabl
%O A104382 1,5
%A A104382 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 04 2005