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A185946 Exponential Riordan array (e^(x), x*A000108(x)). 2

%I

%S 1,1,1,1,4,1,1,21,9,1,1,184,90,16,1,1,2425,1210,250,25,1,1,42396,

%T 21195,4640,555,36,1,1,916909,458451,103355,13475,1071,49,1,1,

%U 23569456,11784724,2705696,370790,32816,1876,64,1,1,701312049,350656020,81531156,11544246,1091286,70644,3060,81,1,1,23697421300,11848710645,2780716800,402965850,39827592,2789850,138720,4725,100,1

%N Exponential Riordan array (e^(x), x*A000108(x)).

%H G. C. Greubel, <a href="/A185946/b185946.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=1, R(n,0,1) = 1.

%e Array begins

%e 1;

%e 1, 1;

%e 1, 4, 1;

%e 1, 21, 9, 1;

%e 1, 184, 90, 16, 1;

%e 1, 2425, 1210, 250, 25, 1;

%e 1, 42396, 21195, 4640, 555, 36, 1;

%e 1, 916909, 458451, 103355, 13475, 1071, 49, 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_] = 1; Table[r[n, k, 1], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-Fran├žois Alcover_, Jun 14 2013, after _Vladimir Kruchinin_ *)

%Y Cf. A000108.

%K nonn,tabl

%O 0,5

%A _Vladimir Kruchinin_, Feb 07 2011

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Last modified May 17 05:13 EDT 2021. Contains 343965 sequences. (Running on oeis4.)