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 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

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