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

%I A185946 #25 Feb 19 2025 10:25:37
%S A185946 1,1,1,1,4,1,1,21,9,1,1,184,90,16,1,1,2425,1210,250,25,1,1,42396,
%T A185946 21195,4640,555,36,1,1,916909,458451,103355,13475,1071,49,1,1,
%U A185946 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 A185946 Exponential Riordan array (e^(x), x*A000108(x)).
%H A185946 G. C. Greubel, <a href="/A185946/b185946.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H A185946 Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F A185946 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 A185946 Array begins
%e A185946   1;
%e A185946   1,      1;
%e A185946   1,      4,      1;
%e A185946   1,     21,      9,      1;
%e A185946   1,    184,     90,     16,      1;
%e A185946   1,   2425,   1210,    250,     25,      1;
%e A185946   1,  42396,  21195,   4640,    555,     36,      1;
%e A185946   1, 916909, 458451, 103355,  13475,   1071,     49,      1;
%t A185946 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-François Alcover_, Jun 14 2013, after _Vladimir Kruchinin_ *)
%Y A185946 Cf. A000108.
%K A185946 nonn,tabl
%O A185946 0,5
%A A185946 _Vladimir Kruchinin_, Feb 07 2011