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A007744 Expansion of (1+6*x)/(1-4*x)^(7/2). 3
1, 20, 210, 1680, 11550, 72072, 420420, 2333760, 12471030, 64664600, 327202876, 1622493600, 7909656300, 38003792400, 180324117000, 846321189120, 3934071152550, 18132120329400, 82937661506700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fourth column in A104684. - Paul Barry, May 02 2005

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

A. Petojevic and N. Dapic, The vAm(a,b,c;z) function, Preprint 2013

G. Thimm, Emails to N. J. A. Sloane, Sep. 1994

FORMULA

a(n) = binomial(2n+3, n) * binomial(n+3, 3). - Paul Barry, May 02 2005

G.f.: G(0) where G(k) = 1 + 4*x*(k+1)*(4*k+5)/((2*k+1)^2 - x*(2*k+1)^2*(2*k+3)*(4*k+7)/(x*(2*k+3)*(4*k+7) + 2*(k+1)^2/G(k+1))); (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Jul 12 2012

D-finite with recurrence: n*a(n) + 2*(n-11)*a(n-1) + 12*(-2*n-1)*a(n-2) = 0. - R. J. Mathar, Nov 24 2012

PROG

(MAGMA) [Binomial(2*n+3, n)*Binomial(n+3, 3): n in [0..20]]; // Vincenzo Librandi, Aug 20 2011

CROSSREFS

Sequence in context: A126905 A341236 A022585 * A304023 A219467 A121204

Adjacent sequences:  A007741 A007742 A007743 * A007745 A007746 A007747

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)