A185948 Exponential Riordan array (e^(mx),x*A000108(x)), m=3.

1, 3, 1, 9, 8, 1, 27, 57, 15, 1, 81, 480, 186, 24, 1, 243, 5505, 2550, 450, 35, 1, 729, 87048, 42795, 8760, 915, 48, 1, 2187, 1780569, 887733, 194355, 23625, 1659, 63, 1, 6561, 44326656, 22154580, 5010768, 660870, 54432, 2772, 80, 1, 19683, 1291851585, 645896268, 148808772, 20586258, 1862406, 112140, 4356, 99, 1, 59049, 43011249480, 21505526325, 5015422800, 715608810, 68717376, 4590810, 212400, 6525, 120, 1

Offset

0,2

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,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=3, R(n,0,1)=3^n.

Example

[1]
[3,1]
[9,8,1]
[27,57,15,1]
[81,480,186,24,1]
[243,5505,2550,450,35,1]
[729,87048,42795,8760,915,48,1]
[2187,1780569,887733,194355,23625,1659,63,1]

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_] = 3^n; Table[R[n, k, 3], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Jul 23 2017 *)

Crossrefs

Sequence in context: A136320 A201840 A114195 * A016601 A193031 A078416

Adjacent sequences: A185945 A185946 A185947 * A185949 A185950 A185951

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Feb 07 2011

Status

approved