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A372020
G.f. A(x) satisfies A(x) = ( 1 + 16*x*A(x)/(1 - x*A(x)) )^(1/4).
2
1, 4, -4, 4, 156, -1212, 5628, 196, -251620, 2500484, -12608772, 16004, 671151260, -7039845180, 37258827516, 1585476, -2133978944740, 23052545651460, -125166709730820, 174117124, 7480512144282780, -82265332158299580, 453899597102224380, 20390254020
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 16^k * binomial(n/4+1/4,k) * binomial(n-1,n-k).
PROG
(PARI) a(n) = sum(k=0, n, 16^k*binomial(n/4+1/4, k)*binomial(n-1, n-k))/(n+1);
CROSSREFS
Cf. A372005.
Sequence in context: A077725 A217940 A353000 * A182065 A325487 A239351
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 15 2024
STATUS
approved