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A177782 G.f. A(x) satisfies: [x^n] A_{2^(n-1)}(x) = 0 for n>2 where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x. 1
1, 2, -12, 56, -12080, -9802944, -31002027840, -344291147482368, -13751106868604649216, -2036529273026085671952640, -1148515664060697951003807202304 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Paul D. Hanna, Table of n, a(n), n = 1..50.

EXAMPLE

G.f.: A(x) = x + 2*x^2 - 12*x^3 + 56*x^4 - 12080*x^5 +...

Coefficients in the (2^n)-th iterations of A(x), n=0..7, begin:

[1, 2, -12, 56, -12080, -9802944, -31002027840, ...];

[1, 4, -16, 0, -23296, -19776000, -62160338944, ...];

[1, 8, 0, -256, -47104, -40198144, -124955000832, ...];

[1, 16, 128, 0, -106496, -83165184, -252519120896, ...];

[1, 32, 768, 14336, 0, -175898624, -516100718592, ...];

[1, 64, 3584, 184320, 8454144, 0, -1064313028608, ...];

[1, 128, 15360, 1777664, 199622656, 21145583616, 0, ...];

[1, 256, 63488, 15482880, 3730571264, 888894652416, 205351244791808, 0, ...];

where the zeros along the diagonal illustrate the property

that the coefficient of x^n in A_{2^(n-1)} is zero for n>2.

PROG

(PARI) {a(n)=local(A=[1, 2], G); for(m=3, n, A=concat(A, 0); G=x*Ser(A); for(i=2, m, G=subst(G, x, G)); A[ #A]=-polcoeff(G, #A)/(2^(#A-1))); A[n]}

CROSSREFS

Sequence in context: A256150 A180073 A067125 * A005038 A094780 A268594

Adjacent sequences:  A177779 A177780 A177781 * A177783 A177784 A177785

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 17 2010

STATUS

approved

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Last modified February 25 21:00 EST 2020. Contains 332258 sequences. (Running on oeis4.)