OFFSET
0,2
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) = (n!/(k-1)!) * Sum_{i=0..(n-k)} (m^i/i!)*binomial(2*(n-i)-k-1,n-i-1)/(n-i), k>0, m=2, R(n,0,1) = 2^n.
EXAMPLE
[1]
[2,1]
[4,6,1]
[8,36,12,1]
[16,296,132,20,1]
[32,3600,1760,340,30,1]
[64,60192,30000,6400,720,42,1]
[128,1271872,635712,141680,17920,1344,56,1]
MATHEMATICA
R[n_, k_, m_] := (n!/(k - 1)!)*Sum[m^i/i!*Binomial[2*(n - i) - k - 1, n - i - 1]/(n - i), {i, 0, n - k}]; R[n_, 0, m_] = 2^n; Table[R[n, k, 2], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Jul 23 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 07 2011
STATUS
approved