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 A358952 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(2*n) * (x^n - 2*A(x))^(3*n+1). 9
 1, 2, 18, 124, 1244, 11652, 122153, 1281722, 14009973, 154993908, 1748602308, 19949674928, 230299666100, 2682127476280, 31492460744869, 372295036400060, 4428101312591810, 52949362040059258, 636176332781478365, 7676183282453865394, 92978971123440688904 (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 Paul D. Hanna, Table of n, a(n) for n = 0..200 FORMULA G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies: (1) 0 = Sum_{n=-oo..+oo} x^(2*n) * (x^n - 2*A(x))^(3*n+1). (2) 0 = Sum_{n=-oo..+oo} x^(3*n*(n-1)) / (1 - 2*A(x)*x^n)^(3*n-1). a(n) ~ c * d^n / n^(3/2), where d = 13.043520100475... and c = 0.432996977380... - Vaclav Kotesovec, Dec 08 2022 EXAMPLE G.f.: A(x) = 1 + 2*x + 18*x^2 + 124*x^3 + 1244*x^4 + 11652*x^5 + 122153*x^6 + 1281722*x^7 + 14009973*x^8 + 154993908*x^9 + 1748602308*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^(2*n) * (x^n - 2*Ser(A))^(3*n+1) ), #A-1)/2); A[n+1]} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A355865, A358953, A358954, A358955, A358956, A358957, A358958, A358959. Sequence in context: A342124 A289830 A361304 * A060589 A325275 A277661 Adjacent sequences: A358949 A358950 A358951 * A358953 A358954 A358955 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 07 2022 STATUS approved

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Last modified May 22 14:42 EDT 2024. Contains 372755 sequences. (Running on oeis4.)