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 A353326 Series reversion of x*(1 - x^2)^8*(1 + x^2)*(1 + 6*x^2 + x^4). 3
 1, 1, 24, 95, 2699, 15803, 426524, 3152930, 78893000, 687247207, 16006168608, 157792378176, 3453454403373, 37490799893638, 778751573489764, 9127308648236072, 181560354411764773, 2263213799047242089, 43447241664660806352, 569330835658843131787 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS See various formulas in A353324, which is essentially the same as this sequence (after dropping the initial term along with zero coefficients). LINKS Paul D. Hanna, Table of n, a(n) for n = 1..1000 EXAMPLE G.f.: A(x) = x + x^3 + 24*x^5 + 95*x^7 + 2699*x^9 + 15803*x^11 + 426524*x^13 + 3152930*x^15 + 78893000*x^17 + 687247207*x^19 + ... where Series_Reversion(A(x)) = x*(1 - x^2)^8*(1 + x^2)*(1 + 6*x^2 + x^4) = x - x^3 - 21*x^5 + 85*x^7 - 134*x^9 + 70*x^11 + 70*x^13 - 134*x^15 + 85*x^17 - 21*x^19 - x^21 + x^23. Related series. (1 + A(x))^8 = 1 + 8*x + 28*x^2 + 64*x^3 + 126*x^4 + 416*x^5 + 1680*x^6 + 5248*x^7 + 13973*x^8 + 53008*x^9 + ... + A353326(n)*x^n + ... where 1 + A(x) is the g.f. of A353324. PROG (PARI) {a(n) = my(A = serreverse(x*(1 - x^2)^8*(1 + x^2)*(1 + 6*x^2 + x^4) +x*O(x^(2*n)) )); polcoeff(A, 2*n-1)} for(n=1, 20, print1(a(n), ", ")) CROSSREFS Cf. A353324, A353325. Sequence in context: A179962 A076799 A297540 * A055671 A090214 A283446 Adjacent sequences:  A353323 A353324 A353325 * A353327 A353328 A353329 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 14 2022 STATUS approved

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Last modified August 13 05:18 EDT 2022. Contains 356077 sequences. (Running on oeis4.)