A281429 - OEIS

%I #7 May 21 2017 11:31:06

%S 1,1,1,5,17,145,865,10325,88865,1357825,15335425,284963525,3993275825,

%T 87274812625,1462392957025,36716097543125,716611617346625,

%U 20309401097610625,452780458211706625,14290053364475013125,358439197464543820625,12462411363013047060625

%N E.g.f.: C(x) + S(x) = exp( Integral C(x)^4 dx ) where C(x) and S(x) is described by A281428 and A281427, respectively.

%e E.g.f: C(x) + S(x) = 1 + x + x^2/2! + 5*x^3/3! + 17*x^4/4! + 145*x^5/5! + 865*x^6/6! + 10325*x^7/7! + 88865*x^8/8! + 1357825*x^9/9! + 15335425*x^10/10! + 284963525*x^11/11! + 3993275825*x^12/12! + 87274812625*x^13/13! + 1462392957025*x^14/14! + 36716097543125*x^15/15! + 716611617346625*x^16/16! + 20309401097610625*x^17/17! + 452780458211706625*x^18/18! + 14290053364475013125*x^19/19! + 358439197464543820625*x^20/20! +...

%e where log( C(x) + S(x) ) = Integral C(x)^4 dx, and

%e C(x)^4 = 1 + 4*x^2/2! + 104*x^4/4! + 6880*x^6/6! + 855680*x^8/8! + 171673600*x^10/10! + 50628300800*x^12/12! + 20616410214400*x^14/14! + 11081874771968000*x^16/16! + 7600553402810368000*x^18/18! + 6477130108444835840000*x^20/20! +...

%o (PARI) {a(n) = my(S=x, C=1); for(i=0, n, S = intformal( C^5 +x*O(x^n)); C = 1 + intformal( S*C^4 ) ); n!*polcoeff(C+S, n)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A281427, A281428.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Feb 01 2017