A212381 G.f. satisfies: A(x) = x^2 + d/dx A(A(x))/2.

1, 2, 10, 78, 728, 7848, 94374, 1242910, 17696008, 269931648, 4382342380, 75347334440, 1366637858280, 26068366769840, 521600687481182, 10924123724430678, 239025078013012744, 5454868593441272080, 129644175575638999380, 3204394919259792492432

Offset

2,2

Links

Table of n, a(n) for n=2..21.

Formula

G.f. A(x) satisfies: A(A(x)) = Sum_{n>=4} 2*a(n-1)/n * x^n.

G.f. satisfies: A(x) = x^2 + A'(x)*A'(A(x))/2.

Example

G.f.: A(x) = x^2 + 2*x^3 + 10*x^4 + 78*x^5 + 728*x^6 + 7848*x^7 +...
such that
A(A(x)) = x^4 + 4*x^5 + 26*x^6 + 208*x^7 + 1962*x^8 + 20972*x^9 + 248582*x^10 + 3217456*x^11 + 44988608*x^12 +...+ 2*a(n-1)*x^(n+1)/(n+1) +...
Related expansions:
A'(x) = 2*x + 6*x^2 + 40*x^3 + 390*x^4 + 4368*x^5 + 54936*x^6 +...
A'(A(x)) = 2*x^2 + 4*x^3 + 26*x^4 + 180*x^5 + 1640*x^6 + 17112*x^7 +...

Prog

(PARI) {a(n)=local(A=x^2+x^3); for(i=1, n, A=x^2+deriv(subst(A, x, A+x*O(x^n)))/2); polcoeff(A, n)}
for(n=2, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A355471 A240599 A367142 * A098692 A300994 A307722

Adjacent sequences: A212378 A212379 A212380 * A212382 A212383 A212384

Keyword

nonn

Author

Paul D. Hanna, May 11 2012

Status

approved