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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A358953 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(3*n) * (x^n - 2*A(x))^(4*n+1). 7
 1, 3, 21, 159, 1369, 12131, 111489, 1042310, 9878188, 94345595, 905236045, 8698907855, 83509981377, 798911473287, 7596665295846, 71585365842419, 666055801137389, 6089025714101416, 54304588402962717, 467144137463862047, 3798557443794080777, 27983895459969702990 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Related identity: 0 = Sum_{n=-oo..+oo} x^n * (y - x^n)^n, which holds formally for all y. LINKS Table of n, a(n) for n=0..21. FORMULA G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies: (1) 0 = Sum_{n=-oo..+oo} x^(3*n) * (x^n - 2*A(x))^(4*n+1). (2) 0 = Sum_{n=-oo..+oo} x^(4*n*(n-1)) / (1 - 2*A(x)*x^n)^(4*n-1). EXAMPLE G.f.: A(x) = 1 + 3*x + 21*x^2 + 159*x^3 + 1369*x^4 + 12131*x^5 + 111489*x^6 + 1042310*x^7 + 9878188*x^8 + 94345595*x^9 + 905236045*x^10 + ... PROG (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = polcoeff( sum(n=-#A, #A, x^(3*n) * (x^n - 2*Ser(A))^(4*n+1) ), #A-1)/2); A[n+1]} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A355865, A358952, A358954, A358955, A358956, A358957, A358958, A358959. Sequence in context: A205773 A192364 A286918 * A189508 A074570 A136781 Adjacent sequences: A358950 A358951 A358952 * A358954 A358955 A358956 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 07 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 December 7 05:59 EST 2023. Contains 367630 sequences. (Running on oeis4.)