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A065140 2^n*(2*n)!. 3
1, 4, 96, 5760, 645120, 116121600, 30656102400, 11158821273600, 5356234211328000, 3278015337332736000, 2491291656372879360000, 2301953490488540528640000, 2541356653499348743618560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,100

FORMULA

Hypergeometric generating function, in Maple notation: 1/sqrt(1-8*x), i.e. a(0)=1, a(n)=round(evalf(subs(x=0, n!*diff(1/(sqrt(1-8*x)), x$n)))), n=1, 2... Integral representation as n-th moment of a positive function on a positive half-axis: a(n)=int(x^n*exp(-sqrt(x/2))/(2*sqrt(2*x)), x=0..infinity), n=0, 1....

G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 4*x*(k+1)*(2*k+1)/(4*x*(k+1)*(2*k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 07 2013

MATHEMATICA

Table[2^n (2n)!, {n, 0, 15}] (* Harvey P. Dale, Nov 28 2011 *)

PROG

(PARI) { for (n=0, 100, write("b065140.txt", n, " ", 2^n*(2*n)!) ) } [From Harry J. Smith, Oct 11 2009]

CROSSREFS

Sequence in context: A077155 A013042 A190196 * A007106 A111637 A027872

Adjacent sequences:  A065137 A065138 A065139 * A065141 A065142 A065143

KEYWORD

nonn

AUTHOR

Karol A. Penson, Oct 16 2001

STATUS

approved

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Last modified March 26 00:51 EDT 2017. Contains 284111 sequences.