A371426 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 - x^3) ).

1, 2, 5, 13, 34, 87, 212, 471, 858, 740, -3674, -29291, -141951, -576379, -2111677, -7161898, -22646026, -66408560, -176815194, -403468266, -641064024, 337909918, 9269952852, 55908644837, 256989808831, 1033152002312, 3792152422259, 12903091079930, 40749582818221

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Index entries for reversions of series

Formula

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

Prog

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

Crossrefs

Cf. A001006, A371427.

Cf. A369212.

Sequence in context: A122024 A252932 A318234 * A027931 A218481 A267905

Adjacent sequences: A371423 A371424 A371425 * A371427 A371428 A371429

Keyword

sign

Author

Seiichi Manyama, Mar 23 2024

Status

approved