A185814 Exponential Riordan array (e^x,A005043(x))

1, 1, 1, 1, 2, 1, 1, 9, 3, 1, 1, 52, 30, 4, 1, 1, 545, 250, 70, 5, 1, 1, 6966, 3615, 740, 135, 6, 1, 1, 114457, 56301, 13895, 1715, 231, 7, 1, 1, 2199464, 1107148, 255416, 40390, 3416, 364, 8, 1, 1, 49219137, 24542820, 5904444, 856926, 98406, 6132, 540, 9, 1

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2013.

Formula

R(n,k) = (n!/(k-1)!)*Sum_{i=0..(n-k)} 1/i!*(Sum_{j=k..(n-i)} binomial(2*j-k-1,j-1)*(-1)^(n-j-i)*binomial(n-i,j))/(n-i), k>0, R(n,0)=1.

Example

[1]
[1,1]
[1,2,1]
[1,9,3,1]
[1,52,30,4,1]
[1,545,250,70,5,1]
[1,6966,3615,740,135,6,1]
[1,114457,56301,13895,1715,231,7,1]

Mathematica

r[n_, 0] := 1; r[n_, k_] := (n!/(k - 1)!)*Sum[(1/i!)*Sum[Binomial[2*j - k - 1, j - 1]*(-1)^(n - j - i)*Binomial[n - i, j], {j, k, n - i}]/(n - i), {i, 0, n - k}]; Table[r[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Jul 14 2017 *)

Crossrefs

Sequence in context: A332717 A260374 A157109 * A174553 A167015 A124522

Adjacent sequences: A185811 A185812 A185813 * A185815 A185816 A185817

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Feb 05 2011

Status

approved