OFFSET
0,3
REFERENCES
L. Comtet and M. Fiolet, Sur les dérivées successives d'une fonction implicite. C. R. Acad. Sci. Paris Ser. A 278 (1974), 249-251.
FORMULA
a(n) = n*((-1)^n*3F1(1,1,1-n;2;-1)+3F1(1,1,1-n;2;1))/2, n>0. - Benedict W. J. Irwin, May 30 2016
a(n) ~ (-1)^n * (n-1)! * sinh(1). - Vaclav Kotesovec, May 30 2016
a(n) = (-1)^n * Sum_{k=1..floor(n/2)} (n-2*k)! * binomial(n,2*k-1). - Seiichi Manyama, Feb 12 2025
EXAMPLE
log(1+x) * sinh(x) = x^2 -x^3/2 +x^4/2 -x^5/3 +19*x^6/72 -17*x^7/80 +...
MAPLE
A177699 := proc(n)
log(1+x)*sinh(x) ;
coeftayl(%, x=0, n)*n! ;
end proc;
seq(A177699(n), n=0..20) ; # R. J. Mathar, Nov 07 2011
MATHEMATICA
Table[n ((-1)^n HypergeometricPFQ[{1, 1, 1 - n}, {2}, -1] + HypergeometricPFQ[{1, 1, 1 - n}, {2}, 1])/2, {n, 1, 20}] (* Benedict W. J. Irwin, May 30 2016 *)
PROG
(PARI) a(n) = (-1)^n*sum(k=1, n\2, (n-2*k)!*binomial(n, 2*k-1)); \\ Seiichi Manyama, Feb 12 2025
CROSSREFS
KEYWORD
sign
AUTHOR
Michel Lagneau, May 11 2010
STATUS
approved