A185947 Exponential Riordan array (e^(mx),x*A000108(x)), m=2.

1, 2, 1, 4, 6, 1, 8, 36, 12, 1, 16, 296, 132, 20, 1, 32, 3600, 1760, 340, 30, 1, 64, 60192, 30000, 6400, 720, 42, 1, 128, 1271872, 635712, 141680, 17920, 1344, 56, 1, 256, 32241792, 16120384, 3677632, 495600, 42448, 2296, 72, 1, 512, 950337792, 475167744, 110026560, 15416352, 1428336, 89376, 3672, 90, 1, 1024, 31890752000, 15945373440, 3731228160, 536833920, 52353504, 3586800, 172320, 5580, 110, 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=2, R(n,0,1) = 2^n.

Example

[1]
[2,1]
[4,6,1]
[8,36,12,1]
[16,296,132,20,1]
[32,3600,1760,340,30,1]
[64,60192,30000,6400,720,42,1]
[128,1271872,635712,141680,17920,1344,56,1]

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_] = 2^n; Table[R[n, k, 2], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Jul 23 2017 *)

Crossrefs

Sequence in context: A075497 A158983 A261642 * A268472 A079474 A091543

Adjacent sequences: A185944 A185945 A185946 * A185948 A185949 A185950

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Feb 07 2011

Status

approved