OFFSET
0,7
COMMENTS
Essentially A139375 with zero diagonal added. - Ralf Stephan, Jan 01 2014
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2013.
FORMULA
For m=1: R(n,k,m) = k*Sum_{i=0..n-k} (Sum_{j=ceiling((i-m)/2)..i-m} binomial(j, i-m-j) * binomial(m+j-1, m-1)) * binomial(2*(n-i)-k-1, n-i-1)/(n-i) if k > 0; R(n,0,m) = Sum_{j=ceiling((n-m)/2)..n-m} binomial(j, n-m-j) * binomial(m+j-1, m-1).
EXAMPLE
Array begins
0;
1, 0;
1, 1, 0;
2, 2, 1, 0;
3, 5, 3, 1, 0;
5, 12, 9, 4, 1, 0;
8, 31, 26, 14, 5, 1, 0;
13, 85, 77, 46, 20, 6, 1, 0;
MATHEMATICA
r[n_, k_, m_] := k*Sum[ Sum[ Binomial[j, i-m-j]*Binomial[m+j-1, m-1], {j, Ceiling[(i-m)/2], i-m}] * Binomial[2*(n-i)-k-1, n-i-1]/(n-i), {i, 0, n-k}]; r[n_, 0, m_] := Sum[ Binomial[j, n-m-j]*Binomial[m+j-1, m-1], {j, Ceiling[(n-m)/2], n-m}]; Table[r[n, k, 1], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 14 2013, after Vladimir Kruchinin *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 06 2011
STATUS
approved