A369507 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^3)^2 ).

1, 6, 51, 508, 5535, 63888, 767689, 9502254, 120324606, 1551362160, 20296839585, 268785905790, 3595951246855, 48528885742200, 659856371680971, 9031161933443468, 124319953470044970, 1720113658097639532, 23908612149570793386, 333680424238179500976

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..849

Robert Israel, Recurrence of order 7

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-3*k).

D-finite with recurrence of order 7 (see link). - Robert Israel, Jul 01 2026

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^3)^2)/x)
(PARI) a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-3*k))/(n+1);

Crossrefs

Cf. A369483, A369504.

Sequence in context: A199685 A225615 A002295 * A215159 A263895 A027393

Adjacent sequences: A369504 A369505 A369506 * A369508 A369509 A369510

Keyword

nonn,changed

Author

Seiichi Manyama, Jan 25 2024

Status

approved