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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.)