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A184896
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a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+1)*(7k+6).
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6
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1, 84, 45864, 35672000, 32445913500, 32247604076688, 33935228690034672, 37165308416775931392, 41919854708375196052500, 48365506771435816732770000, 56812832722107710740048677120, 67715433011522917282547695380480
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..11.
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FORMULA
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Self-convolution of A184895, where A184895(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+1)*(14k+6).
a(n) ~ sin(Pi/7) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - Vaclav Kotesovec, Oct 23 2020
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EXAMPLE
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G.f.: A(x) = 1 + 84*x + 45864*x^2 + 35672000*x^3 +...
A(x)^(1/2) = 1 + 42*x + 22050*x^2 + 16909900*x^3 +...+ A184895(n)*x^n +...
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PROG
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(PARI) {a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0, n-1, (7*k+1)*(7*k+6))}
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CROSSREFS
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Cf. A184895; variants: A184423, A008977, A184892, A001421, A184898.
Sequence in context: A184126 A185403 A269897 * A203093 A290274 A289557
Adjacent sequences: A184893 A184894 A184895 * A184897 A184898 A184899
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Jan 25 2011
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STATUS
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approved
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