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A210723
E.g.f. A(x) satisfies the property that the coefficient of x^n in the (3*n)-th iteration of e.g.f. A(x), n>=1, begins with [1,6] and continues with all zeros thereafter.
2
1, 2, -48, 2508, -195720, 19394280, -2206441440, 267051279600, -33344060611680, 4780804499402400, -902528268205132800, 97427878696933646400, 39689742093333546614400, 44617592399752410588950400, -47223291860874418982172480000
OFFSET
0,2
EXAMPLE
E.g.f.: A(x) = x + 2*x^2/2! - 48*x^3/3! + 2508*x^4/4! - 195720*x^5/5! + 19394280*x^6/6! - 2206441440*x^7/7! + 267051279600*x^8/8! +...
Coefficients of x^k/k! in the (3*n)-th iteration of the g.f. A(x) begin:
n=3: [1, 6, -108, 4860, -330480, 27556200, -2391878160, ...];
n=6: [1, 12, -108, 3888, -204120, 10147680, 135943920, ...];
n=9: [1, 18, 0, 972, -29160, -3936600, 1212472800, ...];
n=12:[1, 24, 216, 0, 19440, -5248800, 771573600, ...];
n=15:[1, 30, 540, 4860, 0, -2187000, 157988880, ...];
n=18:[1, 36, 972, 19440, 204120, 0, -121247280, ...];
n=21:[1, 42, 1512, 47628, 1156680, 20207880, 0, ...];
n=24:[1, 48, 2160, 93312, 3615840, 122472000, 3189170880, 0, ...]; ...
where the main diagonal consists of all zeros for n>2.
PROG
(PARI) {ITERATE(n, F)=local(G=x); for(i=1, n, G=subst(G, x, F)); G}
{a(n)=local(A=[1, 2]); for(m=3, n, A=concat(A, 0); A[#A]=-(#A-1)!/3*Vec(ITERATE(3*(#A), sum(k=1, #A-1, A[k]*x^k/k!)+x*O(x^#A)))[#A]); A[n]}
for(n=1, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A177317 A114714 A186416 * A346454 A322750 A367537
KEYWORD
sign
AUTHOR
Paul D. Hanna, Aug 31 2013
STATUS
approved