0,2

Let G(x) be the g.f. of A134046 where [x^n] G(x)^(2^n) = 4^n,

then G(x) put to powers 2^n, n=0..6, begin as follows:

G(x)^1 = 1 + 2x - 2x^2 - 20x^3 - 394x^4 - 72756x^5 - 38636660x^6 +...;

G(x)^2 = (1) + 4x + 0x^2 - 48x^3 - 864x^4 -147008x^5 - 77562368x^6 +...;

G(x)^4 = 1 + (8)x +16x^2 - 96x^3 -2112x^4 -300928x^5 -156298496x^6 +...;

G(x)^8 = 1 +16x + (96)x^2 +64x^3 -5504x^4 -638720x^5 -317470208x^6 +...;

G(x)^16= 1 +32x+448x^2+(3200)x^3 + 256x^4-1441280x^5 -656432128x^6 +...;

G(x)^32= 1+64x+1920x^2+35072x^3+(406016)x^4 +1024x^5-1394636800x^6 +...;

G(x)^64= 1+128x+7936x^2+315904x^3+8987648x^4+(186648576)x^5+4096x^6+...;

where coefficients in parenthesis, divided by respective powers of 4,

form the initial terms of this sequence.

(PARI) {a(n)=local(A=[]); for(i=0, n, A=concat(A, 0); A[i+1]=(4^i - Vec(Ser(A)^(2^i))[i+1])/2^i); Vec(Ser(A)^(2^(n+1)))[n+1]/4^n}

Cf. A134046.

Sequence in context: A103990 A079835 A052332 this_sequence A078464 A108905 A027263

Adjacent sequences: A134044 A134045 A134046 this_sequence A134048 A134049 A134050

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2007