

A116679


Triangle read by rows: T(n,k) is the number of partitions of n into distinct part and having exactly k even parts (n>=0, k>=0).


1



1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 2, 3, 1, 2, 4, 2, 2, 5, 3, 2, 6, 4, 3, 7, 4, 1, 3, 8, 6, 1, 3, 10, 8, 1, 4, 11, 10, 2, 5, 13, 11, 3, 5, 15, 14, 4, 5, 18, 18, 5, 6, 20, 21, 7, 7, 23, 24, 9, 1, 8, 26, 29, 12, 1, 8, 30, 36, 14, 1, 9, 34, 41, 18, 2, 11, 38, 47, 23, 3, 12, 43, 55, 28, 4
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OFFSET

0,10


COMMENTS

Row n contains floor((1+sqrt(1+4n))/2) terms. Row sums yield A000009. T(n,0)=A000700(n). T(n,1)=A096911(n) (n>=1). Sum(k*T(n,k), k>=0)=A116680(n).


LINKS

Table of n, a(n) for n=0..89.


FORMULA

G.f.=product((1+x^(2j1))(1+tx^(2j)), j=1..infinity).


EXAMPLE

T(9,2)=2 because we have [6,2,1] and [4,3,2].
Triangle starts:
1;
1;
0,1;
1,1;
1,1;
1,2;
1,2,1;
1,3,1;


MAPLE

g:=product((1+x^(2*j1))*(1+t*x^(2*j)), j=1..25): gser:=simplify(series(g, x=0, 38)): P[0]:=1: for n from 1 to 27 do P[n]:=sort(coeff(gser, x^n)) od: for n from 0 to 27 do seq(coeff(P[n], t, j), j=0..floor((sqrt(1+4*n)1)/2)) od; # yields sequence in triangular form


CROSSREFS

Cf. A000009, A000700, A096911, A116680.
Sequence in context: A233932 A008289 A188884 * A146290 A135539 A129264
Adjacent sequences: A116676 A116677 A116678 * A116680 A116681 A116682


KEYWORD

nonn,tabf


AUTHOR

Emeric Deutsch, Feb 22 2006


STATUS

approved



