A222146 - OEIS

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A222146

a(n) = n-th third-order hyperharmonic-exponential number, multiplied by n!.

0, 1, 9, 116, 2082, 49774, 1525752, 58180632, 2694333744, 148623965136, 9611353576800, 719080605842400, 61545135592056960, 5968396255982428800, 650359540100397012480, 79053322881277342886400, 10650510963204404347238400, 1581353364394671905218406400

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

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) * H3(k)) * A000142(n) 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, alpha=3) = sum(k=0, n, n!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k, alpha));