A371394 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+3*x)^3 ).

1, 10, 137, 2174, 37562, 686004, 13027065, 254641398, 5089756958, 103552330700, 2137385941418, 44647634773420, 942085264713556, 20050276273007080, 429913404536172633, 9278142975370425510, 201383222768034837750, 4393265621094818733660

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+3*x)^3)/x)
(PARI) a(n) = sum(k=0, n, 3^k*binomial(3*(n+1), k)*binomial(2*n-k, n-k))/(n+1);

Crossrefs

Cf. A082298, A371393.

Cf. A365816.

Sequence in context: A376064 A276131 A003377 * A230344 A348137 A318594

Adjacent sequences: A371391 A371392 A371393 * A371395 A371396 A371397

Keyword

nonn

Author

Seiichi Manyama, Mar 21 2024

Status

approved