A070256 Define P(n,X) by the recursion P(1,X) = 1, P(n+1,X) = (P(n,X)+X)^2; then a(1) = 0 and for n > 1 a(n) is the coefficient of X^(2^(n-2)) in P(n,X) of degree 2^(n-1).

0, 2, 11, 207, 99919, 32416037103, 4788545326929179011183, 147201835861247697127798679336116306013028335, 196331785117316517420778884783875086749917195699904294273499082962835791812062775501401839

Offset

1,2

Comments

a(n) is the greatest coefficient in P(n,X). Next term is too large to include.

Links

Table of n, a(n) for n=1..9.

Formula

For n > 4, 2^(2^(n-1)) < a(n) < (5/2)^(2^(n-1)).

Example

P(1,X) = 1 then P(2,X) = (1+X)^2 = X^2+2X+1, the coefficient of X^(2^(2-2)) = X is 2 = a(2). P(4,X) = x^8+12*x^7+58*x^6+146*x^5+207*x^4+166*x^3+71*x^2+14*x+1 and the coefficient of X^(2^(4-2)) = X^4 is 207 = a(4).

Prog

(PARI) u=1; for(n=2, 6, a=(u+x)^2; u=a; print1(polcoeff(u, 2^(n-2), x), ", "))

Crossrefs

Sequence in context: A348859 A358649 A188203 * A356523 A020450 A036229

Adjacent sequences: A070253 A070254 A070255 * A070257 A070258 A070259

Keyword

easy,nonn

Author

Benoit Cloitre, May 09 2002

Status

approved