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 A134046 G.f. A(x) satisfies: [x^n] A(x)^(2^n) = 4^n for n>=0. 2
 1, 2, -2, -20, -394, -72756, -38636660, -62621451464, -320115036508314, -5370757579794299764, -307243789286348665328060, -61750332256061511777753774808, -44549932891827456895274618101297860, -117151486172958209318246658698308578710856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..13. FORMULA A134047(n) = [x^n] A(x)^( 2^(n+1) ) / 4^n. G.f. A(x) satisfies: 1/(1-4x) = Sum_{n>=0} log( A(2^n*x) )^n / n! = 1 + log(A(2x)) + log(A(4x)^2/2! + log(A(8x))^3/3! +... - Paul D. Hanna, Jan 05 2008 EXAMPLE To illustrate the property [x^n] A(x)^(2^n) = 4^n, put the g.f. A(x) to powers 2^n, n=0..6, as follows: A(x)^1 = (1) + 2x - 2x^2 - 20x^3 - 394x^4 - 72756x^5 - 38636660x^6 +...; A(x)^2 = 1 + (4)x + 0x^2 - 48x^3 - 864x^4 -147008x^5 - 77562368x^6 +...; A(x)^4 = 1 + 8x +(16)x^2 - 96x^3 -2112x^4 -300928x^5 -156298496x^6 +...; A(x)^8 = 1 +16x + 96x^2 +(64)x^3 -5504x^4 -638720x^5 -317470208x^6 +...; A(x)^16= 1 +32x +448x^2 +3200x^3+(256)x^4-1441280x^5 -656432128x^6 +...; A(x)^32= 1 +64x+1920x^2+35072x^3+406016x^4+(1024)x^5-1394636800x^6 +...; A(x)^64= 1+128x+7936x^2+315904x^3+8987648x^4+186648576x^5+(4096)x^6+...; where coefficients enclosed in parenthesis are successive powers of 4. PROG (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); A[n+1]} CROSSREFS Cf. A134047. Sequence in context: A002907 A350466 A184717 * A081687 A082811 A014353 Adjacent sequences: A134043 A134044 A134045 * A134047 A134048 A134049 KEYWORD sign AUTHOR Paul D. Hanna, Oct 25 2007 STATUS approved

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Last modified August 3 21:27 EDT 2024. Contains 374905 sequences. (Running on oeis4.)