|
| |
|
|
A098665
|
|
Sum(k=0..n, binomial(n,k) * binomial(n+1,k+1) * 4^k).
|
|
2
|
|
|
|
1, 6, 43, 332, 2661, 21810, 181455, 1526040, 12939145, 110413406, 947052723, 8157680228, 70518067309, 611426078346, 5315138311383, 46308989294640, 404274406256145, 3535479068797110, 30966952059306555, 271616893912241532, 2385412594943633781, 20973327081776664546
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Fifth binomial transform of A098664.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..200
|
|
|
FORMULA
|
G.f.: ((1+3*x)-sqrt(1-10*x+9*x^2))/(8*x*sqrt(1-10*x+9*x^2)).
E.g.f.: exp(5x)*(BesselI(0, 4x)+BesselI(1, 4x)/2).
Recurrence: (n+1)*(2*n-1)*a(n) = 4*(5*n^2-2)*a(n-1) - 9*(n-1)*(2*n+1)*a(n-2). - Vaclav Kotesovec, Oct 15 2012
a(n) ~ 9^(n+1)/(4*sqrt(2*Pi*n)). - Vaclav Kotesovec, Oct 15 2012
|
|
|
MATHEMATICA
|
Table[SeriesCoefficient[((1+3*x)-Sqrt[1-10*x+9*x^2])/(8*x*Sqrt[1-10*x+9*x^2]), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 15 2012 *)
|
|
|
PROG
|
(PARI) x='x+O('x^66); Vec(((1+3*x)-sqrt(1-10*x+9*x^2))/(8*x*sqrt(1-10*x+9*x^2))) \\ Joerg Arndt, May 12 2013
|
|
|
CROSSREFS
|
Sequence in context: A091129 A091128 A025594 * A153397 A005786 A071541
Adjacent sequences: A098662 A098663 A098664 * A098666 A098667 A098668
|
|
|
KEYWORD
|
easy,nonn,changed
|
|
|
AUTHOR
|
Paul Barry, Sep 20 2004
|
|
|
STATUS
|
approved
|
| |
|
|
