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A366023
Expansion of (1/x) * Series_Reversion( x*(1-x)*(1+x^4) ).
2
1, 1, 2, 5, 13, 36, 104, 309, 940, 2915, 9184, 29328, 94747, 309180, 1017824, 3376693, 11279274, 37906330, 128085630, 434913555, 1483226921, 5078436800, 17450556480, 60159492600, 208013078910, 721205983737, 2506764055592, 8733076109732, 30489081691750
OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+k,n) * binomial(2*n-4*k,n).
MATHEMATICA
CoefficientList[InverseSeries[Series[x(1-x)(1+x^4), {x, 0, 29}], x]/x, x] (* Stefano Spezia, Sep 26 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, n)*binomial(2*n-4*k, n))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 26 2023
STATUS
approved