A227886 G.f. A(x) satisfies: prime(n-1) iteration of A(x) yields a zero coefficient of x^n for n>2.

1, 1, -2, 6, -24, -820, 27144, -1291488, 59107938, -3469468244, -551251146312, 110380085358300, -14603070221993568, 1245952635117666628, 29007906387788967008, -20843885535528328473491, -180339645015007436197752, 127321605693530805940344950, 281613877399819446654643101264

Offset

1,3

Links

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

Example

G.f.: A(x) = x + x^2 - 2*x^3 + 6*x^4 - 24*x^5 - 820*x^6 + 27144*x^7 +...
Coefficients in the prime iterations of A(x) begin:
[1,  2,  -2,    3,    -10,   -1818,    47740,  -2337494,  105376812, ...];
[1,  3,   0,   -3,      0,   -2772,    60624,  -3189473,  140910696, ...];
[1,  5,  10,    0,    -40,   -4650,    64048,  -4546444,  185930620, ...];
[1,  7,  28,   63,      0,   -6958,    36288,  -5825281,  201609418, ...];
[1, 11,  88,  561,   2816,       0,   -88880, -10110089,  134676036, ...];
[1, 13, 130, 1092,   7800,   34658,        0, -13180700,   29207048, ...];
[1, 17, 238, 2958,  33320,  327012,  2674984,         0, -240789190, ...];
[1, 19, 304, 4389,  58368,  703988,  7570512,  51417135,          0, ...];
[1, 23, 460, 8487, 147200, 2401338, 36774976, 501489263, 5774993410, 0, ...]; ...
where the coefficient of x^n in the prime(n-1) iteration of A(x) equals zero for n>2.

Prog

(PARI) {ITERATION(n, F)=local(G=x); for(i=1, n, G=subst(G, x, F)); G}
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(ITERATION(prime(#A-1), x*Ser(A)))[#A]/prime(#A-1)); A[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A061774 A110729 A088258 * A290961 A089718 A123150

Adjacent sequences: A227883 A227884 A227885 * A227887 A227888 A227889

Keyword

sign

Author

Paul D. Hanna, Oct 25 2013

Status

approved