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.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A283536 Expansion of exp( Sum_{n>=1} -A283535(n)/n*x^n ) in powers of x. 5
1, -1, -64, -19619, -16755517, -30499543213, -101528172949440, -558442022082754554, -4721800698082895269442, -58144976385942395405449505, -999941534906642496357956893139, -23224150593200781968944997552887957, -708778584588517237886357058373629079824 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{k>=1} (1 - x^k)^(k^(3*k)).
a(n) = -(1/n)*Sum_{k=1..n} A283535(k)*a(n-k) for n > 0.
MATHEMATICA
A[n_] := Sum[d^(3*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, 12}] (* Indranil Ghosh, Mar 11 2017 *)
PROG
(PARI) A(n) = sumdiv(n, d, d^(3*d + 1));
a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, A(k)*a(n - k)));
for(n=0, 12, 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), A283534 (m=2), this sequence (m=3).
Cf. A283580 (Product_{k>=1} 1/(1 - x^k)^(k^(3*k))).
Sequence in context: A330482 A187407 A271241 * A089208 A083282 A082502
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 14:43 EDT 2024. Contains 372952 sequences. (Running on oeis4.)