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A369581
Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)^2) ).
1
1, 1, 1, 1, 2, 4, 7, 11, 20, 40, 79, 147, 278, 550, 1110, 2204, 4352, 8708, 17689, 35971, 72933, 148271, 303582, 624132, 1283898, 2643354, 5458457, 11306443, 23460067, 48727689, 101363663, 211262307, 441026328, 921743772, 1928573045, 4040272335, 8474803721
OFFSET
0,5
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(n-3*k+1,n-4*k).
PROG
(PARI) my(N=40, 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+1, k)*binomial(n-3*k+1, n-4*k))/(n+1);
CROSSREFS
Cf. A367414.
Sequence in context: A160393 A018173 A288380 * A146156 A304916 A024927
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 26 2024
STATUS
approved