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Search: id:A127776
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| A127776 |
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( (2^n / n!) * product[ k=0..n-1 ] (4*k + 1) )^2. |
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+0
1
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| 1, 4, 100, 3600, 152100, 7033104, 344622096, 17582760000, 924193822500, 49701090010000, 2721631688947600, 151241747739534400, 8507348310348810000, 483459012855561960000, 27715027900230072360000
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of K(k)/(pi/2) in powers of (kk'/4)^2, where K(k) is complete elliptic integral of first kind evaluated at modulus k.
Expansion of 1/AGM(1, (1-16x)^(1/2) ) in powers of x(1-16x) where AGM() is the arithmetic-geometric mean.
G.f.: F(1/4, 1/4; 1; 64x).
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, prod(k=1, n, (8*k-6)/k)^2)}
(PARI) {a(n)=local(A); if(n<1, n==0, A=x*O(x^n); polcoeff( subst( 1/agm(1, sqrt(1-16*x+A) ), x, serreverse( x*(1-16*x)+A )), n))}
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CROSSREFS
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a(n)=A004981(n)^2. Convolution square is A002987.
Sequence in context: A017090 A029995 A052144 this_sequence A059105 A129435 A129702
Adjacent sequences: A127773 A127774 A127775 this_sequence A127777 A127778 A127779
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jan 14 2007
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