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A369478
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^2)^2) ).
2
1, 4, 24, 170, 1320, 10868, 93197, 823484, 7445184, 68545882, 640446224, 6057249180, 57878746750, 557903174040, 5418441862824, 52971933934834, 520869559359424, 5147999004530720, 51113415228327827, 509583784051748692, 5099262428810825568
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(4*n-k+4,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x+x^2)^2))/x)
(PARI) a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
CROSSREFS
Cf. A369441.
Sequence in context: A374659 A221088 A365225 * A368975 A366980 A369471
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 23 2024
STATUS
approved