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).

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, 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, 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

Offset: 0

Author

Emeric Deutsch, Mar 06 2006

Keywords

• nonn
• tabl

Comments

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).

Examples

			T(8,2)=3 because we have [6,1,1],[4,2,1,1] and [3,3,1,1].
		

Crossrefs

Cf. A001935, A117275, A117276.

Programs

Maple

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

Formula

G.f.=G(t,x)=(1+x^2)*product((1+x^(2k))/(1-x^(2k-1)), k=2..infinity)/(1-tx).