login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A222064 a(n) = n-th third-order hypergeometric-harmonic number. 4
0, 1, 8, 69, 674, 7455, 92540, 1276569, 19394870, 321982323, 5801055632, 112753640109, 2352074473226, 52419496769991, 1243115350746404, 31257697673933889, 830700701852539742, 23266435856618600859, 684997785857198880056, 21149644833172896698709 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.

FORMULA

a(n) = Sum_{k=0..n} A008277(n,k)*A000142(k)*H3(k) where H3(k) is defined by g.f.:- log(1-x)/(1-x)^3.  - Michel Marcus, Feb 09 2013

PROG

(PARI)

hyp(n, alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y); }

a(n) = {sum(k=0, n, k!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k, 3)); }

\\ Michel Marcus, Feb 09 2013

CROSSREFS

Cf. A222057-A222064. Row sums of A222063.

Sequence in context: A214344 A228421 A152109 * A317096 A327606 A226597

Adjacent sequences:  A222061 A222062 A222063 * A222065 A222066 A222067

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 08 2013

EXTENSIONS

More terms from Michel Marcus, Feb 09 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)