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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). 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,16

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).

LINKS

Table of n, a(n) for n=0..103.

FORMULA

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

EXAMPLE

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

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

CROSSREFS

Cf. A001935, A117275, A117276.

Sequence in context: A318133 A068029 A158208 * A221650 A140883 A214021

Adjacent sequences:  A117271 A117272 A117273 * A117275 A117276 A117277

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Mar 06 2006

STATUS

approved

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Last modified September 21 05:55 EDT 2020. Contains 337267 sequences. (Running on oeis4.)