The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A283534 Expansion of exp( Sum_{n>=1} -A283533(n)/n*x^n ) in powers of x. 5
 1, -1, -16, -713, -64687, -9688545, -2165715003, -675843665621, -280752874575386, -149800127959983890, -99844730502381895830, -81300082280849836639246, -79413710313923588156379547, -91652445699847071535357000689, -123383623610527054787988720527285, -191626051373071219208574650313032502 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..214 FORMULA G.f.: Product_{k>=1} (1 - x^k)^(k^(2*k)). a(n) = -(1/n)*Sum_{k=1..n} A283533(k)*a(n-k) for n > 0. MATHEMATICA A[n_] := Sum[d^(2*d + 1), {d, Divisors[n]}]; a[n_] := If[n==0, 1, -(1/n)*Sum[A[k]*a[n - k], {k, n}]]; Table[a[n], {n, 0, 13}] (* Indranil Ghosh, Mar 11 2017 *) PROG (PARI) a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, sumdiv(k, d, d^(2*d + 1))*a(n - k))); for(n=0, 15, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 11 2017 CROSSREFS Cf. Product_{k>=1} (1 - x^k)^(k^(m*k)): A010815 (m=0), A283499 (m=1), this sequence (m=2), A283536 (m=3). Cf. A283579 (Product_{k>=1} 1/(1 - x^k)^(k^(2*k))). Sequence in context: A036513 A123824 A198283 * A294704 A264114 A356482 Adjacent sequences: A283531 A283532 A283533 * A283535 A283536 A283537 KEYWORD sign AUTHOR Seiichi Manyama, Mar 10 2017 STATUS approved

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

Last modified June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)