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

%I

%S 1,1,-2,6,-24,-820,27144,-1291488,59107938,-3469468244,-551251146312,

%T 110380085358300,-14603070221993568,1245952635117666628,

%U 29007906387788967008,-20843885535528328473491,-180339645015007436197752,127321605693530805940344950,281613877399819446654643101264

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

%H Paul D. Hanna, <a href="/A227886/b227886.txt">Table of n, a(n) for n = 1..100</a>

%e G.f.: A(x) = x + x^2 - 2*x^3 + 6*x^4 - 24*x^5 - 820*x^6 + 27144*x^7 +...

%e Coefficients in the prime iterations of A(x) begin:

%e [1, 2, -2, 3, -10, -1818, 47740, -2337494, 105376812, ...];

%e [1, 3, 0, -3, 0, -2772, 60624, -3189473, 140910696, ...];

%e [1, 5, 10, 0, -40, -4650, 64048, -4546444, 185930620, ...];

%e [1, 7, 28, 63, 0, -6958, 36288, -5825281, 201609418, ...];

%e [1, 11, 88, 561, 2816, 0, -88880, -10110089, 134676036, ...];

%e [1, 13, 130, 1092, 7800, 34658, 0, -13180700, 29207048, ...];

%e [1, 17, 238, 2958, 33320, 327012, 2674984, 0, -240789190, ...];

%e [1, 19, 304, 4389, 58368, 703988, 7570512, 51417135, 0, ...];

%e [1, 23, 460, 8487, 147200, 2401338, 36774976, 501489263, 5774993410, 0, ...]; ...

%e where the coefficient of x^n in the prime(n-1) iteration of A(x) equals zero for n>2.

%o (PARI) {ITERATION(n,F)=local(G=x);for(i=1,n,G=subst(G,x,F));G}

%o {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]}

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

%K sign

%O 1,3

%A _Paul D. Hanna_, Oct 25 2013

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Last modified November 15 13:56 EST 2019. Contains 329149 sequences. (Running on oeis4.)