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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

Table of n, a(n) for n=1..18.

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: A125862 A077460 A001205 * 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 November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)