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%I #13 Jul 23 2017 21:44:13
%S 1,2,1,4,6,1,8,36,12,1,16,296,132,20,1,32,3600,1760,340,30,1,64,60192,
%T 30000,6400,720,42,1,128,1271872,635712,141680,17920,1344,56,1,256,
%U 32241792,16120384,3677632,495600,42448,2296,72,1,512,950337792,475167744,110026560,15416352,1428336,89376,3672,90,1,1024,31890752000,15945373440,3731228160,536833920,52353504,3586800,172320,5580,110,1
%N Exponential Riordan array (e^(mx),x*A000108(x)), m=2.
%H G. C. Greubel, <a href="/A185947/b185947.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2013.
%F 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.
%e [1]
%e [2,1]
%e [4,6,1]
%e [8,36,12,1]
%e [16,296,132,20,1]
%e [32,3600,1760,340,30,1]
%e [64,60192,30000,6400,720,42,1]
%e [128,1271872,635712,141680,17920,1344,56,1]
%t 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 *)
%K nonn,tabl
%O 0,2
%A _Vladimir Kruchinin_, Feb 07 2011
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