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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
 1, 24, 24192, 140507136, 2716743794688, 132091533948616704, 13574624941450494738432, 2619220630292562698311827456, 870703020893737265865222361448448 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA Conjecture: a(n)/2^(4n-1) is an odd integer for n>0. EXAMPLE G.f.: cm4(x)^4 = 1 + 24*x^4/4! + 24192*x^8/8! + 140507136*x^12/12! +... The functions: cm4(x) = 1 + 6*x^4/4! + 2268*x^8/8! + 7434504*x^12/12! + 95227613712*x^16/16! +... sm4(x) = x + 18*x^5/5! + 14364*x^9/9! + 70203672*x^13/13! + 1192064637456*x^17/17! +... satisfy: cm4(x)^4 - sm4(x)^4 = 1 ; d/dx cm4(x) = sm4(x)^3 ; d/dx sm4(x) = cm4(x)^3 . PROG (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))} CROSSREFS Cf. A153300 (cm4(x)), A153301 (sm4(x)), A153302 (cm4(x)^2+sm4(x)^2). Sequence in context: A166338 A258874 A188961 * A272095 A188952 A258901 Adjacent sequences:  A153300 A153301 A153302 * A153304 A153305 A153306 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 03 2009 STATUS approved

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Last modified October 22 03:52 EDT 2018. Contains 316431 sequences. (Running on oeis4.)