LINKS
Paul D. Hanna and Vaclav Kotesovec, <a href="/A112317/b112317_1.txt">Table of n, a(n) for n = 1..300</a> (first 100 terms from Paul D. Hanna)
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Revision History for A112317
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
editing
approved
LINKS
Paul D. Hanna, and Vaclav Kotesovec, <a href="/A112317/b112317_1.txt">Table of n, a(n), for n = 1..300</a> (first 100 terms from Paul D.</a> Hanna)
STATUS
approved
editing
STATUS
editing
approved
PROG
for(n=1, 30, print1(a(n), ", "))
STATUS
approved
editing
AUTHOR
_Paul D. Hanna (pauldhanna(AT)juno.com), _, Sep 03 2005
EXTENSIONS
Added cross-references and comments; name and example changed by _Paul D. Hanna (pauldhanna(AT)juno.com), _, Feb 04 2011
STATUS
proposed
approved
NAME
Coefficients of x^n in the n-th self-composition iteration of (x + x^2) for n>=1.
EXAMPLE
F(x) = (1)*The initial iterations of x + x^2 begin:
F(F(x)) = (1)*x + (2)*x^2 +...;
F(F(F(x))) = x + 3(2)*x^2 + (6)2*x^3 +... x^4;
F(F(F(F(x)))) = x + 43*x^2 + 12(6)*x^3 + (30)9*x^4+ 10*x^5+ 8*x^6+ 4 *x^7+... x^8;
F(F(F(F(F(x))))) = x + 54*x^2 + 2012*x^3 + 70(30)*x^4 + (220)64*x^5 +...;
F(F(F(F(F(F(x)))))) = x + 65*x^2 + 3020*x^3 + 13570*x^4 + 560(220)*x^5 + (2170)*x^6 +...;
F(F(F(F(F(F(x)))))) = x + 6*x^2 + 30*x^3 + 135*x^4 + 560*x^5 + (2170)*x^6 +...;
where the terms in parenthesis illustrate how to form this sequence.
EXTENSIONS
Added cross-references and comments; name and example changed by Paul D. Hanna (pauldhanna(AT)juno.com), Feb 04 2011
STATUS
approved
proposed
LINKS
Paul D. Hanna, <a href="/A112317/b112317.txt">Table of n, a(n), n = 1..100.</a>
KEYWORD
nonn,new
nonn