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A101269
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a(1)=0, a(2)=1 a(n+2)=(8*n^2+2*n+1)*a(n+1)-2*n*(2*n-1)^3*a(n).
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2
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0, 1, 11, 299, 15371, 1285371, 159158691, 27376820379, 6246962876475, 1826295061189275, 665694890795056275, 296004348848796457275, 157710301268790933578475, 99189386694727572925906875
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..14.
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FORMULA
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a(n+1)=(2*n)!*{2*G*binomial(2*n, n)/4^n- integral(t=0, infty, t/cosh(t)^(2*n+1))} where G=0.915965594... is Catalan's constant
Contribution from Johannes W. Meijer, May 24 2009: (Start)
a(n) = (2*n-4)!+(2*n-3)^2*a(n-1) for n= 2, 3, ... with a(1) =0.
(End)
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MATHEMATICA
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RecurrenceTable[{a[1]==0, a[2]==1, a[n]==(8(n-2)^2+2(n-2)+1)a[n-1]- 2(n-2)(2(n-2)-1)^3 a[n-2]}, a, {n, 20}] (* Harvey P. Dale, May 06 2013 *)
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PROG
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(PARI) a(n)=if(n<3, (n+1)%2, (8*(n-2)^2+2*(n-2)+1)*a(n-1)-2*(n-2)*(2*(n-2)-1)^3*a(n-2)) - Benoit Cloitre, Dec 02 2005
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CROSSREFS
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Cf. A006752.
Contribution from Johannes W. Meijer, May 24 2009: (Start)
Equals for n>=1 the first left hand column of the Beta triangle A160480. The second left hand column is A160482.
(End)
Sequence in context: A213256 A067424 A001538 * A012184 A012027 A279181
Adjacent sequences: A101266 A101267 A101268 * A101270 A101271 A101272
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Dec 18 2004
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STATUS
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approved
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