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A103978 Expansion of (sqrt(1-12*x^2)+12*x^2+2*x-1)/(2*x*sqrt(1-12*x^2)). 0
1, 3, 6, 9, 54, 54, 540, 405, 5670, 3402, 61236, 30618, 673596, 288684, 7505784, 2814669, 84440070, 28146690, 956987460, 287096238, 10909657044, 2975361012, 124965162504, 31241290626, 1437099368796, 331638315876, 16581915793800 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

FORMULA

G.f.: 1/sqrt(1-12*x^2)+(1-sqrt(1-12*x^2))/(2*x).

a(n) = sum{k=0..floor(n/2), 3^(n-k) * A000108(k) * C(k+1, n-k)}.

Conjecture: -(n+1)*a(n)+2*(n-1)*a(n-1) +12*(2n-3)*a(n-2) +24(2-n)*a(n-3) + 144*(4-n)*a(n-4)=0. - R. J. Mathar, Dec 14 2011

CROSSREFS

Cf. A025225, A059304, A103973.

Sequence in context: A038224 A133195 A196156 * A073910 A115251 A057241

Adjacent sequences:  A103975 A103976 A103977 * A103979 A103980 A103981

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Feb 23 2005

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Last modified February 15 23:53 EST 2012. Contains 205860 sequences.