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 A299424 G.f. A(x) satisfies: 1 = Sum_{n>=0} binomial((n+1)*(n+2), n) / ((n+1)*(n+2)/2) * x^n / A(x)^((n+1)*(n+2)/2). 1
 1, 2, 3, 16, 214, 4268, 110520, 3493432, 130094524, 5576660656, 270624533544, 14679297273336, 880950418422088, 57999873220558048, 4159207521351394736, 322857188993783461264, 26982279001217007103104, 2416289398989507579797760, 230882321991151748812644944, 23451581238859769517764695488, 2523663354227008958133677737296 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare to: 1 = Sum_{n>=0} binomial(m*(n+1), n)/(n+1) * x^n / (1+x)^(m*(n+1)) holds for fixed m. LINKS Paul D. Hanna, Table of n, a(n) for n = 0..200 EXAMPLE G.g.: A(x) = 1 + 2*x + 3*x^2 + 16*x^3 + 214*x^4 + 4268*x^5 + 110520*x^6 + ... such that 1 = 1/A(x) + 2*x/A(x)^3 + 11*x^2/A(x)^6 + 114*x^3/A(x)^10 + 1827*x^4/A(x)^15 + 40508*x^5/A(x)^21 + 1159587*x^6/A(x)^28 + ... PROG (PARI) {a(n) = my(A=[1]); for(i=1, n, A = Vec(sum(m=0, #A, binomial((m+1)*(m+2), m)/((m+1)*(m+2)/2) * x^m/Ser(A)^((m+1)*(m+2)/2-1) ))); A[n+1]} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A299434. Sequence in context: A052318 A141309 A179442 * A215638 A057997 A290590 Adjacent sequences:  A299421 A299422 A299423 * A299425 A299426 A299427 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 13 2018 STATUS approved

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)