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.

1, 2, -48, 2508, -195720, 19394280, -2206441440, 267051279600, -33344060611680, 4780804499402400, -902528268205132800, 97427878696933646400, 39689742093333546614400, 44617592399752410588950400, -47223291860874418982172480000

Offset

0,2

Links

Table of n, a(n) for n=0..14.

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

Cf. A228508, A186292.

Sequence in context: A177317 A114714 A186416 * A346454 A322750 A367537

Adjacent sequences: A210720 A210721 A210722 * A210724 A210725 A210726

Keyword

sign

Author

Paul D. Hanna, Aug 31 2013

Status

approved