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 A359923 a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n. 2
 1, 1, 6, 15, 69, 376, 1741, 8860, 46044, 245074, 1336538, 7337135, 40736876, 228625148, 1293530435, 7372491383, 42275811853, 243742895280, 1412310750812, 8219298313118, 48023377286364, 281592177442072, 1656522460985914, 9773791391488278, 57824226906859849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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) x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n. (2) x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^(n*(n-1)) * A(x)^(n^2) / (1 + 3*x^n*A(x)^n)^n. EXAMPLE G.f.: A(x) = 1 + x + 6*x^2 + 15*x^3 + 69*x^4 + 376*x^5 + 1741*x^6 + 8860*x^7 + 46044*x^8 + 245074*x^9 + 1336538*x^10 + ... where x = ... + x^6*A(x)^9/(1 + 3*x^3*A(x)^3)^3 - x^2*A(x)^4/(1 + 3*x^2*A(x)^2)^2 + A(x)/(1 + 3*x*A(x)) - 1 + x*(3 + x*A(x)) - x^2*(3 + x^2*A(x)^2)^2 + x^3*(3 + x^3*A(x)^3)^3 + ... + (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n + ... PROG (PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = polcoeff(x - sum(m=-#A, #A, (-1)^(m-1) * x^m * (3 + (x*Ser(A))^m)^m ), #A-1)); A[n+1]} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A359672, A359922. Sequence in context: A298374 A324973 A318555 * A035077 A032164 A177122 Adjacent sequences: A359920 A359921 A359922 * A359924 A359925 A359926 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 18 2023 STATUS approved

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Last modified June 10 05:41 EDT 2023. Contains 363195 sequences. (Running on oeis4.)