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

1, 1, 1, 1, 4, 1, 1, 21, 9, 1, 1, 184, 90, 16, 1, 1, 2425, 1210, 250, 25, 1, 1, 42396, 21195, 4640, 555, 36, 1, 1, 916909, 458451, 103355, 13475, 1071, 49, 1, 1, 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

Offset: 0

Author

Vladimir Kruchinin, Feb 07 2011

Keywords

• nonn
• tabl

Examples

			Array begins
  1;
  1,      1;
  1,      4,      1;
  1,     21,      9,      1;
  1,    184,     90,     16,      1;
  1,   2425,   1210,    250,     25,      1;
  1,  42396,  21195,   4640,    555,     36,      1;
  1, 916909, 458451, 103355,  13475,   1071,     49,      1;
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
• Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Crossrefs

Cf. A000108.

Programs

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_] = 1; Table[r[n, k, 1], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 14 2013, after Vladimir Kruchinin *)

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=1, R(n,0,1) = 1.