A377243 - OEIS

A377243

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

1, -2, 2, 8, 22, 48, 76, 48, -154, -352, 2116, 20912, 105788, 399456, 1232984, 3264864, 8078982, 22932800, 89940116, 425480496, 1972255060, 8297959136, 31541857576, 110645755936, 371840906716, 1259842096320, 4514251269672, 17350150918624, 69640154149816

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..28.

FORMULA

a(n) = 4^n * Sum_{k=0..n} (-1)^k * binomial(1/2,k) * binomial(n-3*k/2-1,n-k).

MATHEMATICA

CoefficientList[Series[Sqrt[1-4x Sqrt[1-4x]], {x, 0, 30}], x] (* Harvey P. Dale, Aug 17 2026 *)

PROG

(PARI) a(n) = 4^n*sum(k=0, n, (-1)^k*binomial(1/2, k)*binomial(n-3*k/2-1, n-k));

CROSSREFS