cp's OEIS Frontend

A026821 Triangular array T read by rows: T(n,k) = number of partitions of n into distinct parts, the least being k, for k=1,2,...,n.

%I A026821 #12 Aug 21 2015 13:29:38
%S A026821 1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,2,1,0,0,0,1,2,1,1,0,0,0,1,3,1,1,0,0,0,
%T A026821 0,1,3,2,1,1,0,0,0,0,1,5,2,1,1,0,0,0,0,0,1,5,3,1,1,1,0,0,0,0,0,1,7,3,
%U A026821 2,1,1,0,0,0,0,0,0,1,8,4,2,1,1,1,0,0,0,0,0,0
%N A026821 Triangular array T read by rows: T(n,k) = number of partitions of n into distinct parts, the least being k, for k=1,2,...,n.
%C A026821 T(n,1) = A025147(n-1). Sum(k*T(n,k),k=1..n) = A092265(n). - _Emeric Deutsch_, Feb 24 2006
%F A026821 T(n, k) = T(n-k, k+1) + ... + T(n-k, n-k) for 1<=k<=m and T(n, k)=0 for m+1<=k<=n-1, where m=[ (n-1)/2 ]; T(n, n)=1 for n >= 1.
%F A026821 G.f.: sum(t^j*x^j*product(1+x^i,i=j+1..infinity),j=1..infinity). - _Emeric Deutsch_, Feb 24 2006
%e A026821 T(11,2)=3 because we have [9,2],[6,3,2] and [5,4,2].
%e A026821 Triangle starts:
%e A026821 1;
%e A026821 0,1;
%e A026821 1,0,1;
%e A026821 1,0,0,1;
%e A026821 1,1,0,0,1;
%p A026821 g:=sum(t^j*x^j*product(1+x^i,i=j+1..50),j=1..50): gser:=simplify(series(g,x=0,18)): for n from 1 to 14 do P[n]:=sort(coeff(gser,x^n)) od: seq(seq(coeff(P[n],t^j),j=1..n),n=1..14); # _Emeric Deutsch_, Feb 24 2006
%Y A026821 Cf. A025147, A092265.
%K A026821 nonn,tabl
%O A026821 1,16
%A A026821 _Clark Kimberling_