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A070256
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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).
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0
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0, 2, 11, 207, 99919, 32416037103, 4788545326929179011183, 147201835861247697127798679336116306013028335, 196331785117316517420778884783875086749917195699904294273499082962835791812062775501401839
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OFFSET
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1,2
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COMMENTS
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a(n) is the greatest coefficient in P(n,X). Next term is too large to include.
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LINKS
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Table of n, a(n) for n=1..9.
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FORMULA
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for n>4 2^(2^n)<a(n)<(5/2)^(2^n)
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EXAMPLE
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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).
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PROG
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(PARI) u=1; for(n=2, 6, a=(u+x)^2; u=a; print1(polcoeff(u, 2^(n-2), x), ", "))
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CROSSREFS
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Sequence in context: A271429 A051663 A188203 * A020450 A036229 A104337
Adjacent sequences: A070253 A070254 A070255 * A070257 A070258 A070259
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre, May 09 2002
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STATUS
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approved
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