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Search: id:A157315
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| A157315 |
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G.f.: A(x) = sin( Sum_{n>=0} 2^((2n+1)^2) * C(2n,n)/4^n * x^(2n+1)/(2n+1) ); alternating zeros omitted. |
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2
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| 2, 84, 2516412, 25131689308776, 73459034127708442263660, 59475400379433834763260101514326040, 12984879931670595437855043594849682375333268239320
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Compare g.f. to the expansion of the inverse sine of x:
asin(x) = Sum_{n>=0} C(2n,n)/4^n * x^(2n+1)/(2n+1).
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EXAMPLE
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G.f.: A(x) = 2*x + 84*x^3 + 2516412*x^5 + 25131689308776*x^7 +...
The inverse sine of A(x) begins:
asin(A(x)) = 2*x + 2^9*(2/4)*x^3/3 + 2^25*(6/4^2)*x^5/5 + 2^49*(20/4^3)*x^7/7 + 2^81*(70/4^4)*x^9/9 +...
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PROGRAM
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(PARI) {a(n)=polcoeff(sin(sum(m=0, n\2, 2^((2*m+1)^2)*binomial(2*m, m)/4^m*x^(2*m+1)/(2*m+1))+x*O(x^n)), n)}
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CROSSREFS
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Cf. A136558, A155200, A000984 (C(2n, n)).
Sequence in context: A065591 A099373 A157063 this_sequence A163971 A078166 A101578
Adjacent sequences: A157312 A157313 A157314 this_sequence A157316 A157317 A157318
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 17 2009
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