A377237 Expansion of 1/sqrt(1 - 4*x/sqrt(1 - 4*x)).
1, 2, 10, 56, 326, 1936, 11644, 70672, 431942, 2654816, 16392564, 101611536, 631938524, 3941350816, 24643020344, 154415141152, 969445760070, 6096812777664, 38401653547204, 242213348616592, 1529642560685684, 9671100898555168, 61208631472013256, 387759384222157152
Offset: 0
Keywords
Programs
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PARI
a(n) = 4^n*sum(k=0, n, (-1)^k*binomial(-1/2, k)*binomial(n-k/2-1, n-k));
Formula
a(n) = 4^n * Sum_{k=0..n} (-1)^k * binomial(-1/2,k) * binomial(n-k/2-1,n-k).
a(n) ~ 2^(n+1) * (1 + sqrt(5))^(n - 1/2) / (5^(1/4) * sqrt(Pi*n)). - Vaclav Kotesovec, May 03 2025