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).

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

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^(2k-1)/[(1-tx^(2k-1))product(1-x^(2i-1), i=1..k-1)], 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*k-1)/(1-t*x^(2*k-1))/product(1-x^(2*i-1), i=1..k-1), 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: A218787 A325336 A060016 * A228360 A303138 A276205

Adjacent sequences: A117405 A117406 A117407 * A117409 A117410 A117411

Keyword

nonn,tabl

Author

Emeric Deutsch, Mar 13 2006

Status

approved