A186292 E.g.f. A(x) satisfies the property that the coefficient of x^n in the (2*n)-th iterations of e.g.f. A(x), for n>=1, begins with [1,4] and continues with all zeros thereafter.

1, 2, -30, 1008, -50760, 3227400, -232071840, 17196863040, -1246907208960, 104187854836800, -13090506064574400, 191142937964563200, 646777849055450112000, 339995571993104227200000, -227122463058126580264320000, -361611207685046931735771648000, 110410149903015181792955526144000

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

G.f.: A(x) = x + 2*x^2/2! - 30*x^3/3! + 1008*x^4/4! - 50760*x^5/5! + 3227400*x^6/6! - 232071840*x^7/7! + 17196863040*x^8/8! +...
Coefficients of x^k/k! in the even iterations of the g.f. A(x) begin:
n=2: [1,  4, -48,  1440, -65280,  3628800,-209986560,  9686476800, ...];
n=4: [1,  8, -48,  1152, -40320,  1336320,  11934720,-11065098240, ...];
n=6: [1, 12,   0,   288,  -5760,  -518400, 106444800,-11752151040, ...];
n=8: [1, 16,  96,     0,   3840,  -691200,  67737600, -3261726720, ...];
n=10:[1, 20, 240,  1440,      0,  -288000,  13870080,  1614735360, ...];
n=12:[1, 24, 432,  5760,  40320,        0, -10644480,  1403781120, ...];
n=14:[1, 28, 672, 14112, 228480,  2661120,         0, -1079285760, ...];
n=16:[1, 32, 960, 27648, 714240, 16128000, 279982080,           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)!/2*Vec(ITERATE(2*(#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, A210723.

Sequence in context: A082653 A332231 A274389 * A273661 A322624 A338044

Adjacent sequences: A186289 A186290 A186291 * A186293 A186294 A186295

Keyword

sign

Author

Paul D. Hanna, Aug 29 2013

Status

approved