|
| |
|
|
A098518
|
|
E.g.f. exp(x)BesselI(1,2sqrt(2)x)/sqrt(2).
|
|
2
| |
|
|
0, 1, 2, 9, 28, 105, 366, 1337, 4824, 17649, 64570, 237545, 875700, 3238105, 11998182, 44550105, 165701168, 617297761, 2302877682, 8602038473, 32168532940, 120425227209, 451253210078, 1692411415161, 6352491269640
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Binomial transform of e.g.f. BesselI(1,2sqrt(2)x)/sqrt(2), or {0,1,0,6,0,40,0,280,0,2016,0,....} with g.f. 2x/(1-8x^2+sqrt(1-8x^2)). The binomial transform of e.g.f. BesselI(1,2sqrt(r)x)/sqrt(r) with g.f. 2x/(1-(2sqrt(r)x)^2+sqrt(1-(2sqrt(r)x)^2)) has g.f. 2x/(1-2x-((2sqrt(r))^2-1)x^2+(1-x)sqrt(1-2x-((2sqrt(r))^2-1)x^2)).
|
|
|
FORMULA
| G.f.: 2x/(1-2x-7x^2+(1-x)sqrt(1-2x-7x^2)); a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k+1)2^k}.
conjecture: (n+1)*a(n) -3*n*a(n-1) -(5*n+3)*a(n-2) +7*(n-2)*a(n-3)=0. - R. J. Mathar, Nov 14 2011
|
|
|
CROSSREFS
| Sequence in context: A026087 A109188 A002532 * A086511 A138912 A002747
Adjacent sequences: A098515 A098516 A098517 * A098519 A098520 A098521
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 12 2004
|
| |
|
|
