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Expansion of 1/sqrt(1 - 4*x/sqrt(1 - 4*x)).
1

%I #9 Oct 21 2024 08:57:59

%S 1,2,10,56,326,1936,11644,70672,431942,2654816,16392564,101611536,

%T 631938524,3941350816,24643020344,154415141152,969445760070,

%U 6096812777664,38401653547204,242213348616592,1529642560685684,9671100898555168,61208631472013256,387759384222157152

%N Expansion of 1/sqrt(1 - 4*x/sqrt(1 - 4*x)).

%F a(n) = 4^n * Sum_{k=0..n} (-1)^k * binomial(-1/2,k) * binomial(n-k/2-1,n-k).

%o (PARI) a(n) = 4^n*sum(k=0, n, (-1)^k*binomial(-1/2, k)*binomial(n-k/2-1, n-k));

%Y Cf. A011782, A377238.

%Y Cf. A377239.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 21 2024