

A280520


Triangle read by rows: T(n,k) = number of increasing sequences of n positive integers with reciprocals adding up to k (k=1,2,...,A055980(n)).


4



1, 0, 1, 6, 1, 72, 6, 2320, 72, 245765, 2320, 151182379, 245765
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OFFSET

1,4


COMMENTS

T(n,k) = 0 for all k > A055980(n).
For n=3,...,11, we have T(n,2) = T(n1,1). However, T(12,2) > T(11,1).
Conjecture: for n in A115515 (i.e., A055980(n+1)=A055980(n)+1), the sequences being enumerated by T(n,A055980(n)) must start with 1. E.g., there is no 10tuple (x_1,x_2,...,x_10) with 1 < x_1 < ... < x_10 and 1/x_1 + ... + 1/x_10 = 2 (=A055980(10)).


LINKS

Table of n, a(n) for n=1..13.


EXAMPLE

Triangle starts with:
n=1: 1
n=2: 0
n=3: 1
n=4: 6, 1
n=5: 72, 6
n=6: 2320, 72
n=7: 245765, 2320
n=8: 151182379, 245765
...


CROSSREFS

Cf. A280518 (row sums), A006585 (column k=1), A156869 (nondecreasing sequences), A280519 (ordered sequences).
Sequence in context: A049385 A266364 A009384 * A051151 A009330 A300512
Adjacent sequences: A280517 A280518 A280519 * A280521 A280522 A280523


KEYWORD

nonn,tabf,more


AUTHOR

Max Alekseyev, Jan 04 2017


STATUS

approved



