OFFSET
0,7
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
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), 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), m = 2.
EXAMPLE
Array begins
0;
0, 0;
1, 0, 0;
2, 1, 0, 0;
5, 3, 1, 0, 0;
10, 9, 4, 1, 0, 0;
20, 24, 14, 5, 1, 0, 0;
38, 64, 44, 20, 6, 1, 0, 0;
MATHEMATICA
R[n_, k_, m_] := k*Sum[Sum[Binomial[j, i - m - j]*Binomial[m - 1 + j, 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[j + m - 1, m - 1], {j, Ceiling[(n - m)/2], n - m}];
Table[R[n, k, 2], {n, 0, 10}, {k, 0, n}] (* G. C. Greubel, Jul 23 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 08 2011
STATUS
approved