A145072 - OEIS

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A145072

G.f. satisfies: A(x) = (1+y)*A(y^2) where y = x*A(x).

1, 1, 2, 5, 15, 48, 163, 573, 2074, 7669, 28860, 110148, 425384, 1659185, 6526791, 25863949, 103151955, 413728474, 1667757766, 6753022725, 27454555171, 112024545382, 458616153319, 1883201461892, 7754348091640, 32010908796160

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

FORMULA

G.f. satisfies: A(x) = A( [z/(1+z)]/A(x) )/(1+z) where z = sqrt(x).

EXAMPLE

A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 48*x^5 + 163*x^6 + 573*x^7 +...

A([x/(1+x)]/A(x^2))/(1+x) = 1 + x^2 + 2*x^4 + 5*x^6 + 15*x^8 + 48*x^10 +...

PROG

(PARI) {a(n)=local(A=1+x); for(n=1, n, A=1/x*serreverse(x/((1+x)*subst(A, x, x^2+x*O(x^n))))); polcoeff(A, n)}