A281429 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.

1, 1, 1, 5, 17, 145, 865, 10325, 88865, 1357825, 15335425, 284963525, 3993275825, 87274812625, 1462392957025, 36716097543125, 716611617346625, 20309401097610625, 452780458211706625, 14290053364475013125, 358439197464543820625, 12462411363013047060625

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Example

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! +...
where log( C(x) + S(x) ) = Integral C(x)^4 dx, and
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! +...

Prog

(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)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A281427, A281428.

Sequence in context: A181922 A177509 A160611 * A286307 A119769 A182066

Adjacent sequences: A281426 A281427 A281428 * A281430 A281431 A281432

Keyword

nonn

Author

Paul D. Hanna, Feb 01 2017

Status

approved