A184576 -id:A184576 - cp's OEIS frontend

A184575 G.f.: A(x) = 1+x(1+x(1+x(...(1+x(...)^(3^n) )...)^27)^9)^3.

1, 1, 3, 30, 892, 76554, 19138212, 14126533902, 31053145918644, 204151364083796877, 4021430292908836847748, 237530957105884844479669995, 42082478775006270167542801189164, 22365250673182738144111737076795384386

Offset: 0

Paul D. Hanna, Jan 17 2011

nonn

Limit a(n)/3^[n(n-1)/2] = 1.361839192264541770366149558100...

			G.f.: A(x) = 1 + x + 3*x^2 + 30*x^3 + 892*x^4 + 76554*x^5 +...
Related functions are defined by:
A(x) = 1 + x*B(x)^3;
B(x) = 1 + x*C(x)^9;
C(x) = 1 + x*D(x)^27;
D(x) = 1 + x*E(x)^81;
E(x) = 1 + x*F(x)^243; ...
where the coefficients in the above functions begin:
B=[1,1,9,279,24870,6324282,4695640434,10341522771762,...];
C=[1,1,27,2538,678708,515666952,1144737153180,7549554318496218,...];
D=[1,1,81,22923,18390510,41861447352,278471836036890,...];
E=[1,1,243,206550,497133612,3393278306694,67693048457727060,...];
F=[1,1,729,1859679,13427919990,274923122390262,16451387497191947778,...].

Cf. A120959, A184576, A184577.

{a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(3^(n-j))); polcoeff(A, n)}

A184577 G.f.: A(x) = 1+x(1+x(1+x(...(1+x(...)^(5^n) )...)^125)^25)^5.

Original entry on oeis.org

1, 1, 5, 135, 17635, 11196380, 35146865626, 549810415675025, 42966178319025765725, 16784792206658535573353275, 32783305434744311217446987595100, 320150590803319511079060107920058643150

Offset: 0

Paul D. Hanna, Jan 17 2011

nonn

Limit a(n)/5^[n(n-1)/2] = 1.153465224918418179626705381295781...

			G.f.: A(x) = 1 + x + 5*x^2 + 135*x^3 + 17635*x^4 + 11196380*x^5 +...
Related functions are defined by:
A(x) = 1 + x*B(x)^5;
B(x) = 1 + x*C(x)^25;
C(x) = 1 + x*D(x)^125;
D(x) = 1 + x*E(x)^625;
E(x) = 1 + x*F(x)^3125; ...
where the coefficients in the above functions begin:
B=[1,1,25,3425,2224175,7020109525,109933742396880,8592795153472287100,...];
C=[1,1,125,85875,278520875,4390379300750,343605429779453150,...];
D=[1,1,625,2148125,34827604375,2744338779394375,1073806035818802734500,...];
E=[1,1,3125,53709375,4353763021875,1715255710695800000,...];
F=[1,1,15625,1342765625,544228190109375,1072040316107238765625,...].

Cf. A120959, A184575, A184576.

{a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(5^(n-j))); polcoeff(A, n)}

cp's OEIS Frontend

A184575 G.f.: A(x) = 1+x(1+x(1+x(...(1+x(...)^(3^n) )...)^27)^9)^3.

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A184577 G.f.: A(x) = 1+x(1+x(1+x(...(1+x(...)^(5^n) )...)^125)^25)^5.

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cp's OEIS Frontend

A184575 G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(3^n) )...)^27)^9)^3.

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A184577 G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(5^n) )...)^125)^25)^5.

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Author

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Examples

Crossrefs

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PARI

A184575 G.f.: A(x) = 1+x(1+x(1+x(...(1+x(...)^(3^n) )...)^27)^9)^3.

A184577 G.f.: A(x) = 1+x(1+x(1+x(...(1+x(...)^(5^n) )...)^125)^25)^5.