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 A212381 G.f. satisfies: A(x) = x^2 + d/dx A(A(x))/2. 0
 1, 2, 10, 78, 728, 7848, 94374, 1242910, 17696008, 269931648, 4382342380, 75347334440, 1366637858280, 26068366769840, 521600687481182, 10924123724430678, 239025078013012744, 5454868593441272080, 129644175575638999380, 3204394919259792492432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS 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: A095789 A134980 A240599 * A098692 A300994 A307722 Adjacent sequences:  A212378 A212379 A212380 * A212382 A212383 A212384 KEYWORD nonn AUTHOR Paul D. Hanna, May 11 2012 STATUS approved

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Last modified August 19 21:19 EDT 2019. Contains 326133 sequences. (Running on oeis4.)