A134047 a(n) = [x^n] G(x)^( 2^(n+1) ) / 4^n, where G(x) is the g.f. of A134046 such that G(x) satisfies: [x^n] G(x)^(2^n) = 4^n for n>=0.

1, 2, 6, 50, 1586, 182274, 70856770, 91955753218, 404598404260610, 6173936430806583298, 333433524033498566071298, 64757369178015130100982820866, 45786845522362297626576735328694274

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Example

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.

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); Vec(Ser(A)^(2^(n+1)))[n+1]/4^n}

Crossrefs

Cf. A134046.

Sequence in context: A357086 A052332 A238596 * A370311 A078464 A108905

Adjacent sequences: A134044 A134045 A134046 * A134048 A134049 A134050

Keyword

nonn

Author

Paul D. Hanna, Oct 25 2007

Status

approved