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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A357158 a(n) = coefficient of x^n in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n * A(x)^n. 5
 1, 2, 4, 28, 129, 784, 4547, 28474, 178947, 1160189, 7599423, 50580502, 339862004, 2306662818, 15774817084, 108652754620, 752854936635, 5244889634762, 36713446985136, 258094902741010, 1821402519619699, 12898863644572142, 91638273993427991, 652926934710002885 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Related identity: 0 = Sum_{n=-oo..+oo, n<>0} n * x^n * (1 - x^n)^(n-1), which holds when 0 < |x| < 1. Related identity: 0 = Sum_{n=-oo..+oo} x^n * (1 - x^n)^n, which holds when 0 < |x| < 1. LINKS Paul D. Hanna, Table of n, a(n) for n = 0..300 FORMULA G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following conditions. (1) 1 = Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n * A(x)^n. (2) 1 = Sum_{n=-oo..+oo} (-1)^(n-1) * n * x^(n*(n-1)) / ((1 - x^n)^n * A(x)^n). EXAMPLE G.f.: A(x) = 1 + 2*x + 4*x^2 + 28*x^3 + 129*x^4 + 784*x^5 + 4547*x^6 + 28474*x^7 + 178947*x^8 + 1160189*x^9 + 7599423*x^10 + 50580502*x^11 + 339862004*x^12 + ... where 1 = ... - 3*(x*A(x))^(-3)/(1 - x^(-3))^4 - 2*(x*A(x))^(-2)/(1 - x^(-2))^3 - (x*A(x))^(-1)/(1 - x^(-1))^2 + 0 + x*A(x) + 2*(x*A(x))^2*(1 - x^2) + 3*(x*A(x))^3*(1 - x^3)^2 + 4*(x*A(x))^4*(1 - x^4)^3 + ... + n*(x*A(x))^n*(1 - x^n)^(n-1) + ... SPECIFIC VALUES. A(1/8) = 1.526583049137946431... A(1/9) = 1.373618404532597561... A(1/10) = 1.3014404438931094722929945... PROG (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = polcoeff( sum(n=-#A, #A, n * x^n * (1 - x^n +x*O(x^#A) )^n * Ser(A)^n ), #A-1) ); A[n+1]} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Sequence in context: A274526 A264667 A356700 * A259134 A117443 A095858 Adjacent sequences: A357155 A357156 A357157 * A357159 A357160 A357161 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 05 2022 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 August 14 09:40 EDT 2024. Contains 375159 sequences. (Running on oeis4.)