A370840 Expansion of (1/x) * Series_Reversion( x * (1/(1-x^3) - x) ).

1, 1, 2, 4, 8, 14, 15, -30, -297, -1442, -5693, -20046, -64765, -192911, -522954, -1236717, -2221422, -848673, 18142403, 122417208, 573446212, 2287694033, 8211900486, 26984131280, 81027339912, 217474121511, 487508197964, 690838844798, -1034716617740

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-3*k+1,k) * binomial(2*n-3*k,n-3*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1-x^3)-x))/x)
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-3*k+1, k)*binomial(2*n-3*k, n-3*k))/(n+1);

Crossrefs

Cf. A370839, A370841.

Cf. A369630.

Sequence in context: A253766 A368490 A076380 * A049133 A063033 A128309

Adjacent sequences: A370837 A370838 A370839 * A370841 A370842 A370843

Keyword

sign

Author

Seiichi Manyama, Mar 03 2024

Status

approved