A353326 Coefficients of odd exponents of series reversion of x*(1 - x^2)^8*(1 + x^2)*(1 + 6*x^2 + x^4).

1, 1, 24, 95, 2699, 15803, 426524, 3152930, 78893000, 687247207, 16006168608, 157792378176, 3453454403373, 37490799893638, 778751573489764, 9127308648236072, 181560354411764773, 2263213799047242089, 43447241664660806352, 569330835658843131787

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 + ... + A353325(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: A076799 A297540 A365191 * A055671 A090214 A283446

Adjacent sequences: A353323 A353324 A353325 * A353327 A353328 A353329

Keyword

nonn

Author

Paul D. Hanna, Apr 14 2022

Extensions

Definition amended by Georg Fischer, Jan 21 2026

Status

approved