A135866 -id:A135866 - cp's OEIS frontend

A135864 G.f. A(x) satisfies A(x) = 1 + 9xA(x)^(1/3).

1, 9, 27, 0, -81, 243, 0, -2916, 10935, 0, -168399, 682344, 0, -11711385, 49364964, 0, -900438201, 3887490915, 0, -73729998576, 323480165085, 0, -6303914878248, 27978933759300, 0, -556251967191492, 2490404893915293, 0, -50276620111538700, 226626845346291663, 0

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Paul D. Hanna, Dec 02 2007

sign

Cf. A135863, A135866, A214668.

PARI
```
a(n)=9^n*binomial(n/3,n)/(1-2*n/3)
```

a(n) = -9^n*binomial(n/3,n)/(2n/3 - 1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^(-1/3)). - Seiichi Manyama, Jun 18 2025

A135865 G.f. A(x) satisfies: A(x) = 1 + x*A(4x)^(1/2).

Original entry on oeis.org

1, 1, 2, 14, 420, 52822, 26933340, 55104785932, 451307797531080, 14787550509729279590, 1938204238967340827449260, 1016173347424012723201485482596, 2131067935523127187022102005624003320

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Paul D. Hanna, Dec 02 2007

nonn

Cf. A135866, A135863.

{a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,4*x)^(1/2));polcoeff(A,n)}

cp's OEIS Frontend

A135864 G.f. A(x) satisfies A(x) = 1 + 9xA(x)^(1/3).

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A135865 G.f. A(x) satisfies: A(x) = 1 + x*A(4x)^(1/2).

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cp's OEIS Frontend

A135864 G.f. A(x) satisfies A(x) = 1 + 9*x*A(x)^(1/3).

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A135865 G.f. A(x) satisfies: A(x) = 1 + x*A(4x)^(1/2).

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PARI

A135864 G.f. A(x) satisfies A(x) = 1 + 9xA(x)^(1/3).