A128318 G.f.: A(x) = 1+x*(1+2x*(1+3x*(...(1+n*x*(...)^2)^2...)^2)^2)^2.

1, 1, 4, 28, 276, 3480, 53232, 955524, 19672320, 456803328, 11810032896, 336463895808, 10473959755008, 353739038360832, 12883270796310528, 503352328766459904, 21001144899441162240, 931963581151516477440, 43832663421577452887040, 2178029362561822117094400, 114014865901176834809333760

Offset: 0

Author

Paul D. Hanna, Mar 07 2007

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x*B(x)^2; B(x) = 1 + 2*x*C(x)^2; C(x) = 1 + 3*x*D(x)^2; D(x) = 1 + 4*x*E(x)^2; E(x) = 1 + 5*x*F(x)^2; F(x) = 1 + 6*x*G(x)^2; ...
where the respective sequences begin:
A=[1,1,4,28,276,3480,53232,955524,19672320,...];
B=[1,2,12,114,1440,22368,409248,8585088,202733760,...];
C=[1,3,24,288,4440,82080,1752000,42178800,1127335680,...];
D=[1,4,40,580,10560,226560,5532960,150570240,4501422240,...];
E=[1,5,60,1020,21420,523320,14399280,437433780,14479664640,...];
F=[1,6,84,1638,38976,1068480,32716992,1098069504,39896236800,...];
G=[1,7,112,2464,65520,1991808,67189248,2469837888,97765355520,...];
H=[1,8,144,3528,103680,3461760,127569600,5098406400,218459165760,...];
		

Links

• Paul D. Hanna and Vaclav Kotesovec, Table of n, a(n) for n = 0..385 (terms 0..200 from Paul D. Hanna)

Crossrefs

Cf. A128319, A268652.

Programs

PARI

{a(n)=local(A=1+(n+1)*x);for(k=0,n,A=1+(n-k+1)*x*A^2 +x*O(x^n));polcoeff(A,n)}
for(n=0, 25, print1(a(n), ", "))

Formula

Conjecture: a(n) ~ n! * (8/3)^n / sqrt(n). - Vaclav Kotesovec, Mar 19 2016