

A097304


Triangle of numbers of partitions of n with m parts which are all odd.


3



1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 3, 0, 2, 0, 1, 0, 1, 0, 3, 0, 3, 0, 2, 0, 1, 0, 1, 1, 0, 4, 0, 3, 0, 2, 0, 1, 0, 1, 0, 3, 0, 5, 0, 3, 0, 2, 0, 1, 0, 1, 1, 0, 5, 0, 5, 0, 3, 0, 2, 0, 1, 0, 1, 0, 4, 0, 6, 0, 5, 0, 3, 0, 2, 0, 1, 0, 1
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OFFSET

1,17


LINKS

Table of n, a(n) for n=1..105.
W. Lang, First 10 rows.


FORMULA

T(n, m) := 0 if 1 <= n < m, else T(n, m) = number of partitions of n with m parts which are all odd. Hence T(2*k, 2*j1) = 0, k >= 1, k >= j >= 1; T(2*k1, 2*j) = 0, k >= 1, k1 >= j >= 1.
G.f.: 1/Product_{j>=1} (1  tx^(2j1)).  Emeric Deutsch, Feb 24 2006


EXAMPLE

[1];
[0,1];
[1,0,1];
[0,1,0,1];
[1,0,1,0,1];
[0,2,0,1,0,1];
...
T(6,2)=2 because 6 = 1+5 = 3+3; T(6,1) = 0 = T(6,3): there are no partitions of 6 into either one or three parts with only odd numbers;
T(6,4)=1 from 6 = 1+1+1+3; T(6,6)=1 from 6 = 1+1+1+1+1+1.


MAPLE

g:=1/product(1t*x^(2*j1), j=1..30)1: gser:=simplify(series(g, x=0, 17)): for n from 1 to 15 do P[n]:=sort(coeff(gser, x^n)) od: seq(seq(coeff(P[n], t^j), j=1..n), n=1..15); # Emeric Deutsch, Feb 24 2006


CROSSREFS

Row sums: A000009 (number of partitions of n into odd parts).
Cf. A008284 (partitions of n into k parts).
Sequence in context: A287179 A236511 A235924 * A136745 A214157 A246720
Adjacent sequences: A097301 A097302 A097303 * A097305 A097306 A097307


KEYWORD

nonn,tabl,easy


AUTHOR

Wolfdieter Lang, Aug 13 2004


STATUS

approved



