A371427 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 - x^4) ).

1, 2, 5, 14, 41, 122, 363, 1066, 3046, 8300, 20791, 43738, 51297, -174406, -1825027, -10480330, -50143510, -218385772, -895007802, -3504952380, -13214355159, -48116028934, -169216483595, -573113441834, -1856620607526, -5675964306988, -15927363432481

Offset

0,2

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)} (-1)^k * binomial(n+1,k) * binomial(2*n-2*k+2,n-4*k).

Prog

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

Crossrefs

Cf. A001006, A371426.

Cf. A369158.

Sequence in context: A116845 A307466 A116849 * A123183 A007051 A124302

Adjacent sequences: A371424 A371425 A371426 * A371428 A371429 A371430

Keyword

sign

Author

Seiichi Manyama, Mar 23 2024

Status

approved