A367413 Expansion of (1/x) * Series_Reversion( x * (1-x-x^3/(1-x)^2) ).

1, 1, 2, 6, 22, 87, 356, 1493, 6398, 27936, 123906, 556734, 2528668, 11590555, 53545932, 249065874, 1165482126, 5482782933, 25914899804, 123009541412, 586121731150, 2802470267460, 13441993044464, 64660400422341, 311861855749484, 1507802756171072, 7306422899878394

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Index entries for reversions of series

Formula

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

From Seiichi Manyama, Nov 27 2024: (Start)

G.f.: exp( Sum_{k>=1} A378464(k) * x^k/k ).

a(n) = (1/(n+1)) * [x^n] 1/(1 - x - x^3/(1 - x)^2)^(n+1). (End)

Prog

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

Crossrefs

Cf. A378464.

Cf. A049140, A054515.

Cf. A378466, A378467.

Sequence in context: A165533 A164651 A279566 * A150261 A308409 A150262

Adjacent sequences: A367410 A367411 A367412 * A367414 A367415 A367416

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2024

Status

approved