The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A156910 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)/(1 - 2^n*x)^n * x^n/n ). 1
 1, 2, 14, 268, 21462, 7872396, 12585797612, 84949155244024, 2379063526056509734, 273414369715003663482380, 128009001272184822673783879332, 242979321424122460096958142064785384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS An example of this logarithmic identity at q=2: Sum_{n>=1} [q^(n^2)/(1 - q^n*x)^n]*x^n/n = Sum_{n>=1} [(1 + q^n)^n - 1]*x^n/n. LINKS FORMULA G.f.: A(x) = (1-x)*exp( Sum_{n>=1} (1 + 2^n)^n * x^n/n ); Equals the first differences of A155201. EXAMPLE G.f.: A(x) = 1 + 2*x + 14*x^2 + 268*x^3 + 21462*x^4 +... log(A(x)) = 2/(1-2*x)*x + 2^4/(1-2^2*x)^2*x^2/2 + 2^9/(1-2^3*x)^3*x^3/3 +... log(A(x)) = (3-1)*x + (5^2-1)*x^2/2 + (9^3-1)*x^3/3 + (17^4-1)*x^4/4 +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 2^(m^2)/(1-2^m*x)^m*x^m/m)+x*O(x^n)), n)} (PARI) /* As First Differences of A155201: */ {a(n)=polcoeff((1-x)*exp(sum(m=1, n+1, (2^m+1)^m*x^m/m)+x*O(x^n)), n)} CROSSREFS Cf. A155201, A155200. Sequence in context: A187654 A280517 A015197 * A279117 A018803 A217474 Adjacent sequences:  A156907 A156908 A156909 * A156911 A156912 A156913 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 17 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 12:43 EDT 2021. Contains 347617 sequences. (Running on oeis4.)