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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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1
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OFFSET
| 1,1
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COMMENTS
| 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
| 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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PROG
| (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
| Cf. A136558, A155200, A000984 (C(2n, n)).
Sequence in context: A205643 A157063 A181119 * A078166 A101578 A041881
Adjacent sequences: A157312 A157313 A157314 * A157316 A157317 A157318
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 17 2009
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