A367414 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^2) ).

1, 1, 2, 5, 15, 51, 187, 715, 2800, 11138, 44846, 182476, 749566, 3105575, 12966165, 54505650, 230508612, 980045835, 4186600220, 17960356014, 77343359518, 334217730014, 1448771849516, 6298222363395, 27452466169243, 119949953637406, 525284132440963

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/4)} binomial(n+k,k) * binomial(2*n-k,n-4*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^4/(1-x)^2))/x)
(PARI) a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n-k, n-4*k))/(n+1);

Crossrefs

Cf. A063021, A367317, A367415.

Sequence in context: A149955 A007581 A124303 * A073525 A369481 A366096

Adjacent sequences: A367411 A367412 A367413 * A367415 A367416 A367417

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2024

Status

approved