This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A317349 G.f. A(x) satisfies: Sum_{n>=0} ( 1/A(x) - (1-x)^n )^n  =  1. 6
 1, 1, 2, 7, 42, 372, 4269, 59047, 946557, 17175289, 347208299, 7730688884, 187911183701, 4951155672353, 140575561645293, 4279249948000903, 139050095246322895, 4804391579357016747, 175902340755219278039, 6803436418471129704925, 277202774381386656583959, 11868116969794805874111831 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..300 FORMULA G.f. A(x) satisfies: (1) 1 = Sum_{n>=0} ( 1/A(x) - (1-x)^n )^n. (2) A(x) = Sum_{n>=0} ( 1/A(x) - (1-x)^(n+1) )^n. (3) 1 = Sum_{n>=0} ( 1/A(x) - (1-x)^(n+1) )^n * (1-x)^(n+1). (4) A(x)^2 = 2*A(x) * [ Sum_{n>=0} (n+1) * ( 1/A(x) - (1-x)^(n+1) )^n ] - [ Sum_{n>=0} (n+1) * ( 1/A(x) - (1-x)^(n+2) )^n ]. (5) A(x) = [ Sum_{n>=1} n*(n+1)/2 * (1-x)^(n+1) * ( 1/Ser(A) - (1-x)^(n+1) )^(n-1) ] / [ Sum_{n>=1} n^2 * (1-x)^n * ( 1/Ser(A) - (1-x)^n )^(n-1) ]. a(n) ~ 2^(log(2)/2 - 5/2) * n^n / (sqrt(1-log(2)) * exp(n) * (log(2))^(2*n+1)). - Vaclav Kotesovec, Aug 06 2018 EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 42*x^4 + 372*x^5 + 4269*x^6 + 59047*x^7 + 946557*x^8 + 17175289*x^9 + 347208299*x^10 + ... such that 1 = 1  +  (1/A(x) - (1-x))  +  (1/A(x) - (1-x)^2)^2  +  (1/A(x) - (1-x)^3)^3  +  (1/A(x) - (1-x)^4)^4  +  (1/A(x) - (1-x)^5)^5  +  (1/A(x) - (1-x)^6)^6  +  (1/A(x) - (1-x)^7)^7  +  (1/A(x) - (1-x)^8)^8  + ... Also, A(x) = 1  +  (1/A(x) - (1-x)^2)  +  (1/A(x) - (1-x)^3)^2  +  (1/A(x) - (1-x)^4)^3  +  (1/A(x) - (1-x)^5)^4  +  (1/A(x) - (1-x)^6)^5  +  (1/A(x) - (1-x)^7)^6  +  (1/A(x) - (1-x)^8)^7  +  (1/A(x) - (1-x)^9)^8  + ... PROG (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, ( 1/Ser(A) - (1-x)^(m+1) )^m ) )[#A]/2 ); A[n+1]} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A317339, A317348, A317340, A317666, A317667 A317668. Sequence in context: A265772 A109172 A131682 * A158840 A038052 A066383 Adjacent sequences:  A317346 A317347 A317348 * A317350 A317351 A317352 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 02 2018 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 December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)