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, 2, -12, 56, -12080, -9802944, -31002027840, -344291147482368, -13751106868604649216, -2036529273026085671952640, -1148515664060697951003807202304

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: A180073 A363402 A067125 * A005038 A094780 A268594

Adjacent sequences: A177779 A177780 A177781 * A177783 A177784 A177785

Keyword

sign

Author

Paul D. Hanna, May 17 2010

Status

approved