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A116799 Triangle read by rows: T(n,k) is the number of partitions of n into odd parts such that the largest part is k (n>=1, k>=1). 2
1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 2, 0, 1, 1, 0, 3, 0, 2, 0, 1, 0, 1, 1, 0, 3, 0, 3, 0, 2, 0, 1, 1, 0, 3, 0, 4, 0, 2, 0, 1, 0, 1, 1, 0, 4, 0, 4, 0, 3, 0, 2, 0, 1, 1, 0, 4, 0, 5, 0, 4, 0, 2, 0, 1, 0, 1, 1, 0, 4, 0, 6, 0, 5, 0, 3, 0, 2, 0, 1, 1, 0, 5, 0, 7, 0, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

COMMENTS

Both rows 2n-1 and 2n have 2n-1 terms. Row sums yield A000009. T(n,2k)=0. T(n,3)=A002264(n). Sum(k*T(n,k),k>=1)=A092322(n).

LINKS

Table of n, a(n) for n=1..105.

FORMULA

G.f.=sum(t^(2j-1)*x^(2j-1)/product(1-x^(2i-1), i=1..j), j=1..infinity).

EXAMPLE

T(10,5)=3 because we have [3,3,3,1], [3,3,1,1,1,1] and [3,1,1,1,1,1,1,1].

Triangle starts:

1;

1;

1,0,1;

1,0,1;

1,0,1,0,1;

1,0,2,0,1;

MAPLE

g:=sum(t^(2*j-1)*x^(2*j-1)/product(1-x^(2*i-1), i=1..j), j=1..40): gser:=simplify(series(g, x=0, 22)): for n from 1 to 16 do P[n]:=sort(coeff(gser, x^n)) od: for n from 1 to 16 do seq(coeff(P[n], t^j), j=1..2*ceil(n/2)-1) od; # yields sequence in triangular form

CROSSREFS

Cf. A000009, A002264, A092322, A116856.

Sequence in context: A177416 A087606 A271368 * A057556 A112761 A284320

Adjacent sequences:  A116796 A116797 A116798 * A116800 A116801 A116802

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Feb 24 2006

STATUS

approved

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Last modified April 24 00:59 EDT 2017. Contains 285338 sequences.