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A180023 G.f. satisfies: Sum_{n>=0} x^n*A_{n}(x) = x + x^2, where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x. 1
1, -1, 1, -2, 4, -10, 26, -72, 205, -590, 1677, -4566, 11303, -22524, 20333, 92383, -483115, -789942, 29930165, -291634772, 1988056726, -10150346269, 30543129468, 98096242950, -2594239257483, 26613170323473, -194454017807169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Paul D. Hanna, Table of n, a(n), n=1..100.

EXAMPLE

G.f.: A(x) = x - x^2 + x^3 - 2*x^4 + 4*x^5 - 10*x^6 + 26*x^7 +...

The table of coefficients in the iterations of g.f. A(x) begins:

[1, 0, 0, 0, 0, 0, 0, 0, 0,...];

[1, -1, 1, -2, 4, -10, 26, -72, 205, -590,...];

[1, -2, 4, -10, 28, -86, 282, -973, 3489, -12881,...];

[1, -3, 9, -30, 108, -414, 1668, -7003, 30426, -136026,...];

[1, -4, 16, -68, 304, -1420, 6884, -34462, 177414, -935984,...];

[1, -5, 25, -130, 700, -3890, 22230, -130250, 780475, -4772240,...];

[1, -6, 36, -222, 1404, -9090, 60126, -405587, 2785695, -19453005,...];

[1, -7, 49, -350, 2548, -18886, 142352, -1089893, 8467424,...];

[1, -8, 64, -520, 4288, -35864, 304008, -2609868, 22675676,...];

[1, -9, 81, -738, 6804, -63450, 598194, -5698812, 54834489,...];

[1, -10, 100, -1010, 10300, -106030, 1101410, -11541225,...]; ...

in which the antidiagonal sums yield [1,1,0,0,0,0,0,...].

PROG

(PARI) {a(n)=local(A=[1], F, G, s); for(j=2, n, A=concat(A, 0); F=x*Ser(A); for(k=1, #A, s=0; G=x; for(i=1, k, G=subst(G, x, F); s+=Vec(G)[k-i+1])); A[ #A]=-s); A[n]}

CROSSREFS

Sequence in context: A149814 A125108 A075864 * A154835 A049145 A102407

Adjacent sequences:  A180020 A180021 A180022 * A180024 A180025 A180026

KEYWORD

sign

AUTHOR

Paul D. Hanna, Aug 14 2010

STATUS

approved

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Last modified February 20 22:47 EST 2020. Contains 332086 sequences. (Running on oeis4.)