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 A112320 Coefficient of x^n in the (n+1)-th iteration of (x + x^2) for n>=1. 4
 1, 3, 12, 70, 560, 5810, 74760, 1153740, 20817588, 430604724, 10052947476, 261595087182, 7509722346204, 235808741944100, 8040824716606176, 295914258931377276, 11690732617035570008, 493527339623630078552 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(n) = [x^n] F_{n+1}(x) where F_{n+1}(x) = F_n(x+x^2) with F_1(x) = x+x^2 and F_0(x)=x for n>=1. EXAMPLE The first few iterations of (x+x^2) begin: F(x) = x + x^2; F(F(x)) = (1)*x + 2*x^2 + 2*x^3 + x^4; F(F(F(x))) = x + (3)*x^2 + 6*x^3 + 9*x^4 + 10*x^5 +...; F(F(F(F(x)))) = x + 4*x^2 + (12)*x^3 + 30*x^4 + 64*x^5 +...; F(F(F(F(F(x))))) = x + 5*x^2 + 20*x^3 + (70)*x^4 + 220*x^5 +...; F(F(F(F(F(F(x)))))) = x + 6*x^2 + 30*x^3 + 135*x^4 + (560)*x^5 +...; coefficients enclosed in parenthesis form the initial terms of this sequence. PROG (PARI) {a(n)=local(F=x+x^2, G=x+x*O(x^n)); if(n<1, 0, for(i=1, n+1, G=subst(F, x, G)); return(polcoeff(G, n, x)))} for(n=1, 25, print1(a(n), ", ")) CROSSREFS Cf. A112317, A112319. Sequence in context: A077460 A001205 A330493 * A103366 A277457 A228386 Adjacent sequences:  A112317 A112318 A112319 * A112321 A112322 A112323 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 06 2005 STATUS approved

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Last modified April 6 15:23 EDT 2020. Contains 333276 sequences. (Running on oeis4.)