|
|
A185946
|
|
Exponential Riordan array (e^(x), x*A000108(x)).
|
|
2
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
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.
|
|
EXAMPLE
|
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;
|
|
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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|