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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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1
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1, 4, 100, 3600, 152100, 7033104, 344622096, 17582760000, 924193822500, 49701090010000, 2721631688947600, 151241747739534400, 8507348310348810000, 483459012855561960000, 27715027900230072360000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| 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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PROG
| (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
| a(n)=A004981(n)^2. Convolution square is A002987.
Sequence in context: A173987 A052144 A165518 * A198278 A202990 A202989
Adjacent sequences: A127773 A127774 A127775 * A127777 A127778 A127779
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Jan 14 2007
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