

A066855


Triangle T(n,k) of numbers of representations of n as a sum of k products of positive integers, k=1..n. 1 is not allowed as a factor, unless it is the only factor.Representations which differ only in the order of terms or factors are considered equivalent.


0



1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 2, 1, 1, 2, 4, 4, 2, 1, 1, 1, 5, 5, 4, 2, 1, 1, 3, 7, 8, 6, 4, 2, 1, 1, 2, 8, 11, 9, 6, 4, 2, 1, 1, 2, 11, 16, 14, 10, 6, 4, 2, 1, 1, 1, 11, 20, 20, 15, 10, 6, 4, 2, 1, 1, 4, 15, 28, 29, 23, 16, 10, 6, 4, 2, 1, 1, 1, 16, 33, 39, 33, 24, 16, 10, 6, 4, 2, 1, 1, 2, 19
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OFFSET

1,7


COMMENTS

Row sums give A066739.


LINKS

Table of n, a(n) for n=1..93.


FORMULA

G.f.: Product_{m=1..infinity} (1y*x^m)^(A001055(m)). T(n, k) = Sum_{pi} Product_{m=1..n} binomial(p(m)+A001055(m)1, p(m)), where pi runs through all nonnegative solutions of p(1)+2*p(2)+...+n*p(n)=n, p(1)+p(2)+...+p(n)=k.


EXAMPLE

[1], [1, 1], [1, 1, 1], [2, 2, 1, 1], [1, 3, 2, 1, 1], ... . For n=5, 5 = 4+1 = 2*2+1 = 3+2 = 3+1+1 = 2+2+1 = 2+1+1+1 = 1+1+1+1+1, giving the batch [1, 3, 2, 1, 1].


CROSSREFS

Cf. A001055, A066739.
Sequence in context: A112468 A207194 A086275 * A175685 A331182 A182591
Adjacent sequences: A066852 A066853 A066854 * A066856 A066857 A066858


KEYWORD

nonn,tabl


AUTHOR

Vladeta Jovovic, Jan 21 2002


STATUS

approved



