A379328 - OEIS

A379328

G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x)^3) * (1 + 2*x*A(x)) ).

1, 2, 8, 44, 272, 1808, 12616, 91136, 675712, 5112576, 39316480, 306402304, 2414543328, 19207303168, 154030314752, 1243912552448, 10107398806016, 82573989969920, 677862373390592, 5588755066388480, 46257005500080128, 384210240316375040, 3201482490107076608

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

FORMULA

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

PROG

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

CROSSREFS

Cf. A379326, A379327.

Cf. A198953, A379280.