This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A224902 O.g.f.: exp( Sum_{n>=1} (sigma(2*n^4) - sigma(n^4)) * x^n/n ). 2
 1, 2, 18, 114, 450, 2298, 10466, 43314, 184402, 749490, 2942274, 11437026, 43364818, 161089130, 589901682, 2123791130, 7531395154, 26360805018, 91057065522, 310718196626, 1048405959266, 3499152601394, 11559430074418, 37818135048962, 122582070331106, 393830310786706, 1254654362883954 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare to the Jacobi theta_3 function: 1 + 2*Sum_{n>=1} x^(n^2)  =  exp( Sum_{n>=1} -(sigma(2*n) - sigma(n))*(-x)^n/n ). Here sigma(n) = A000203(n), the sum of the divisors of n. LINKS FORMULA O.g.f.: exp( Sum_{n>=1} A054785(n^4)*x^n/n ). Logarithmic derivative equals A224903. a(n) == 2 (mod 4) for n>0 (conjecture). EXAMPLE G.f.: A(x) = 1 + 2*x + 18*x^2 + 114*x^3 + 450*x^4 + 2298*x^5 +... where log(A(x)) = 2*x + 32*x^2/2 + 242*x^3/3 + 512*x^4/4 + 1562*x^5/5 +...+ A224903(n)*x^n/n +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, (sigma(2*m^4)-sigma(m^4))*x^m/m)+x^2*O(x^n)), n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A224903, A054785, A000203; variants: A195584, A215603, A225958. Sequence in context: A038721 A308700 A064837 * A027433 A153338 A007798 Adjacent sequences:  A224899 A224900 A224901 * A224903 A224904 A224905 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 24 2013 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 August 21 18:58 EDT 2019. Contains 326168 sequences. (Running on oeis4.)