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A054122
T(2n,n), array T as in A054120.
2
1, 3, 18, 114, 750, 5058, 34692, 240852, 1687446, 11906610, 84490428, 602335836, 4310670156, 30950436468, 222844189320, 1608369633384, 11632913018598, 84294762019218, 611831430746124, 4447397950230540
OFFSET
0,2
LINKS
FORMULA
a(n) = A069835(n) - A069835(n-1).
G.f.: (1-x)/sqrt(1-8*x+4*x^2). - Vladeta Jovovic, May 13 2003
D-finite with recurrence: (n-1)*n*a(n) = 4*(n-1)*(2*n-1)*a(n-1) - 4*(n-2)*n*a(n-2). - Vaclav Kotesovec, Oct 09 2012
a(n) ~ sqrt(6+4*sqrt(3))*(4+2*sqrt(3))^n/(4*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 09 2012
D-finite with recurrence n*a(n) +3*(-3*n+2)*a(n-1) +12*(n-2)*a(n-2) +4*(-n+3)*a(n-3)=0. - R. J. Mathar, Jun 13 2013
MATHEMATICA
Table[SeriesCoefficient[(1-x)/Sqrt[1-8*x+4*x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 09 2012 *)
PROG
(PARI) a(n)=(2*pollegendre(n, 2) - pollegendre(n-1, 2))<<(n-1) \\ Charles R Greathouse IV, Mar 18 2017
CROSSREFS
Cf. A069835.
Sequence in context: A213099 A199259 A163471 * A213230 A201695 A074566
KEYWORD
nonn
STATUS
approved