This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A157315 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. 1
 2, 84, 2516412, 25131689308776, 73459034127708442263660, 59475400379433834763260101514326040, 12984879931670595437855043594849682375333268239320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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). LINKS 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 +... 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)} CROSSREFS Cf. A136558, A155200, A000984 (C(2n, n)). Sequence in context: A215263 A157063 A181119 * A078166 A101578 A041881 Adjacent sequences:  A157312 A157313 A157314 * A157316 A157317 A157318 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 17 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .