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A153303 G.f.: cm4(x)^4 = Sum_{n>=0} a(n)*x^(4n)/(4n)!, where cm4(x) is defined by A153300. 1

%I

%S 1,24,24192,140507136,2716743794688,132091533948616704,

%T 13574624941450494738432,2619220630292562698311827456,

%U 870703020893737265865222361448448

%N G.f.: cm4(x)^4 = Sum_{n>=0} a(n)*x^(4n)/(4n)!, where cm4(x) is defined by A153300.

%F Conjecture: a(n)/2^(4n-1) is an odd integer for n>0.

%e G.f.: cm4(x)^4 = 1 + 24*x^4/4! + 24192*x^8/8! + 140507136*x^12/12! +...

%e The functions:

%e cm4(x) = 1 + 6*x^4/4! + 2268*x^8/8! + 7434504*x^12/12! + 95227613712*x^16/16! +...

%e sm4(x) = x + 18*x^5/5! + 14364*x^9/9! + 70203672*x^13/13! + 1192064637456*x^17/17! +...

%e satisfy:

%e cm4(x)^4 - sm4(x)^4 = 1 ;

%e d/dx cm4(x) = sm4(x)^3 ;

%e d/dx sm4(x) = cm4(x)^3 .

%o (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x); for(i=0, n, A=1+intformal(intformal(A^3)^3)); n=4*n; n!*polcoeff(A^4, n))}

%Y Cf. A153300 (cm4(x)), A153301 (sm4(x)), A153302 (cm4(x)^2+sm4(x)^2).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 03 2009

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Last modified November 28 12:38 EST 2021. Contains 349403 sequences. (Running on oeis4.)