A393926 - OEIS

A393926

a(0) = 1; a(n) = 3 - 2*n + Sum_{k=0..n-1} a(k) * a(n-1-k).

1, 2, 3, 7, 21, 72, 261, 974, 3705, 14306, 55937, 221091, 882107, 3548448, 14377763, 58629311, 240435653, 991013194, 4103273977, 17059167453, 71185826063, 298051854208, 1251772703567, 5272090327112, 22262068842095, 94229389184598, 399731071346335, 1699185944920853

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

FORMULA

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

G.f.: (1 - sqrt(1 - 4*x*(1 + 3*x/(1-x) - 2*x/(1-x)^2)))/(2*x).

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec((1-sqrt(1-4*x*(1+3*x/(1-x)-2*x/(1-x)^2)))/(2*x))

CROSSREFS

Cf. A007317, A086611.