cp's OEIS Frontend

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

%I A153303 #2 Mar 30 2012 18:37:15
%S A153303 1,24,24192,140507136,2716743794688,132091533948616704,
%T A153303 13574624941450494738432,2619220630292562698311827456,
%U A153303 870703020893737265865222361448448
%N A153303 G.f.: cm4(x)^4 = Sum_{n>=0} a(n)*x^(4n)/(4n)!, where cm4(x) is defined by A153300.
%F A153303 Conjecture: a(n)/2^(4n-1) is an odd integer for n>0.
%e A153303 G.f.: cm4(x)^4 = 1 + 24*x^4/4! + 24192*x^8/8! + 140507136*x^12/12! +...
%e A153303 The functions:
%e A153303 cm4(x) = 1 + 6*x^4/4! + 2268*x^8/8! + 7434504*x^12/12! + 95227613712*x^16/16! +...
%e A153303 sm4(x) = x + 18*x^5/5! + 14364*x^9/9! + 70203672*x^13/13! + 1192064637456*x^17/17! +...
%e A153303 satisfy:
%e A153303 cm4(x)^4 - sm4(x)^4 = 1 ;
%e A153303 d/dx cm4(x) = sm4(x)^3 ;
%e A153303 d/dx sm4(x) = cm4(x)^3 .
%o A153303 (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 A153303 Cf. A153300 (cm4(x)), A153301 (sm4(x)), A153302 (cm4(x)^2+sm4(x)^2).
%K A153303 nonn
%O A153303 0,2
%A A153303 _Paul D. Hanna_, Jan 03 2009