

A117408


Triangle read by rows: T(n,k) is the number of partitions of n into odd parts in which the largest part occurs k times (1<=k<=n).


3



1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 1, 5, 1, 1, 0, 0, 0, 0, 0, 1, 6, 2, 1, 0, 0, 0, 0, 0, 0, 1, 8, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 10, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 12, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 15, 4, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

1,11


COMMENTS

Row sums yield A000009. T(n,1)=A117409(n). Sum(k*T(n,k),k=1..n)=A092311(n).


LINKS

Table of n, a(n) for n=1..104.


FORMULA

G.f.=G(t,x)=sum(tx^(2k1)/[(1tx^(2k1))product(1x^(2i1), i=1..k1)], k=1..infinity).


EXAMPLE

T(14,2)=4 because we have [7,7],[5,5,3,1],[5,5,1,1,1,1] and [3,3,1,1,1,1,1,1,1,1].


MAPLE

g:=sum(t*x^(2*k1)/(1t*x^(2*k1))/product(1x^(2*i1), i=1..k1), k=1..40): gser:=simplify(series(g, x=0, 35)): for n from 1 to 15 do P[n]:=expand(coeff(gser, x^n)) od: for n from 1 to 15 do seq(coeff(P[n], t^j), j=1..n) od; # yields sequence in triangular form


CROSSREFS

Cf. A000009, A117409, A092311.
Sequence in context: A218786 A218787 A060016 * A228360 A303138 A276205
Adjacent sequences: A117405 A117406 A117407 * A117409 A117410 A117411


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Mar 13 2006


STATUS

approved



