login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A098411 Expansion of 1/(sqrt(1-4x)sqrt(1-12x)). 1
1, 8, 72, 704, 7264, 77568, 847104, 9394176, 105334272, 1190899712, 13551235072, 154997784576, 1780378353664, 20522842062848, 237284128063488, 2750571189633024, 31956067676454912, 371997834879172608, 4337957919010062336, 50664706036388069376, 592558533060795039744 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Nguyen and Taggart (see link) conjecture: det[a(i+j) for i,j=0..n] = b(n)*b(n+1)/2 with b(n) = A139685(n). - Peter Luschny, May 19 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.

H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014

FORMULA

G.f.: 1/sqrt(1-16x+48x^2).

E.g.f.: exp(8x)*BesselI(0, 4x).

a(n) = Sum_{k=0..n} 3^k*binomial(2k, k)*binomial(2(n-k), n-k).

D-finite with recurrence: n*a(n) +8*(1-2*n)*a(n-1) +48*(n-1)*a(n-2)=0. - R. J. Mathar, Sep 26 2012

a(n) ~ sqrt(3)*12^n/sqrt(2*Pi*n). - Vaclav Kotesovec, Oct 15 2012

a(n) = 4^n*hypergeometric([-n, 1/2], [1], -2). - Peter Luschny, May 19 2015

MATHEMATICA

Table[SeriesCoefficient[1/(Sqrt[1-4*x]*Sqrt[1-12*x]), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 15 2012 *)

PROG

(PARI)  x='x+O('x^66); Vec(1/sqrt(1-16*x+48*x^2)) \\ Joerg Arndt, May 11 2013

(Sage)

a = lambda n: 4^n*hypergeometric([-n, 1/2], [1], -2)

[simplify(a(n)) for n in range(23)] # Peter Luschny, May 19 2015

CROSSREFS

Cf. A098410, A139685.

Sequence in context: A264913 A082414 A145303 * A220741 A165323 A082366

Adjacent sequences:  A098408 A098409 A098410 * A098412 A098413 A098414

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 07 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 19:53 EST 2020. Contains 338965 sequences. (Running on oeis4.)