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A117274 Triangle read by rows: T(n,k) is the number of partitions of n with no even part repeated and having k 1's (n>=0, 0<=k<=n).

%I A117274 #3 Mar 30 2012 17:36:09
%S A117274 1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,2,1,1,1,0,1,3,2,1,1,1,0,1,3,3,2,1,1,1,
%T A117274 0,1,4,3,3,2,1,1,1,0,1,6,4,3,3,2,1,1,1,0,1,7,6,4,3,3,2,1,1,1,0,1,9,7,
%U A117274 6,4,3,3,2,1,1,1,0,1,12,9,7,6,4,3,3,2,1,1,1,0,1,14,12,9,7,6,4,3,3,2,1,1,1,0
%N A117274 Triangle read by rows: T(n,k) is the number of partitions of n with no even part repeated and having k 1's (n>=0, 0<=k<=n).
%C A117274 Row sums yield A001935. T(n,0)=A117275(n). T(n,k)=T(n-k,0)=A117275(n-k). Sum(k*T(n,k),k=0..n)=A117276(n).
%F A117274 G.f.=G(t,x)=(1+x^2)*product((1+x^(2k))/(1-x^(2k-1)), k=2..infinity)/(1-tx).
%e A117274 T(8,2)=3 because we have [6,1,1],[4,2,1,1] and [3,3,1,1].
%p A117274 g:=(1+x^2)*product((1+x^(2*k))/(1-x^(2*k-1)),k=2..50)/(1-t*x): gser:=simplify(series(g,x=0,23)): P[0]:=1: for n from 1 to 14 do P[n]:=sort(coeff(gser,x^n)) od: for n from 0 to 14 do seq(coeff(P[n],t,j),j=0..n) od; # yields sequence in triangular form
%Y A117274 Cf. A001935, A117275, A117276.
%K A117274 nonn,tabl
%O A117274 0,16
%A A117274 _Emeric Deutsch_, Mar 06 2006