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A228508 E.g.f. A(x) satisfies the property that the coefficient of x^n in the n-th iteration of e.g.f. A(x), for n>=1, begins with [1,2] and continues with all zeros thereafter. 3
1, 2, -12, 180, -4080, 113400, -3281040, 75675600, -207930240, -54890589600, -1623047025600, -1372180725115200, 354312481665542400, 98331129549161308800, -22733950460442373152000, -23918355671347608543072000, 1666438721774386195603968000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..120

EXAMPLE

E.g.f.: A(x) = x + 2*x^2/2! - 12*x^3/3! + 180*x^4/4! - 4080*x^5/5! + 113400*x^6/6! - 3281040*x^7/7! + 75675600*x^8/8! - 207930240*x^9/9! - 54890589600*x^10/10! +...

The coefficients of x^k/k!, k>=1, in the n-th iteration of e.g.f. A(x) begin:

n=1: [1,  2, -12,  180,  -4080,  113400,  -3281040,   75675600, ...];

n=2: [1,  4, -12,  144,  -2520,   41760,    186480,  -86446080, ...];

n=3: [1,  6,   0,   36,   -360,  -16200,   1663200,  -91813680, ...];

n=4: [1,  8,  24,    0,    240,  -21600,   1058400,  -25482240, ...];

n=5: [1, 10,  60,  180,      0,   -9000,    216720,   12615120, ...];

n=6: [1, 12, 108,  720,   2520,       0,   -166320,   10967040, ...];

n=7: [1, 14, 168, 1764,  14280,   83160,         0,   -8431920, ...];

n=8: [1, 16, 240, 3456,  44640,  504000,   4374720,          0, ...];

n=9: [1, 18, 324, 5940, 105840, 1798200,  27987120,  343722960, 0, ...]; ...

where the coefficient of x^n in the n-th iteration = 0 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)!*Vec(ITERATE(#A, sum(k=1, #A-1, A[k]*x^k/k!)+x*O(x^#A)))[#A]); A[n]}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Cf. A186292, A210723.

Sequence in context: A156143 A007129 A125861 * A156516 A228593 A067962

Adjacent sequences:  A228505 A228506 A228507 * A228509 A228510 A228511

KEYWORD

sign

AUTHOR

Paul D. Hanna, Aug 23 2013

STATUS

approved

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Last modified February 21 20:35 EST 2020. Contains 332111 sequences. (Running on oeis4.)