A222145 a(n) = n-th second-order hyperharmonic-exponential number, multiplied by n!.

0, 1, 7, 77, 1222, 26364, 739608, 26079780, 1125791280, 58257484128, 3552890064480, 251777905728480, 20488109614761600, 1895120214639868800, 197527783071095930880, 23023412842885582176000, 2980946191374310495795200, 426192103002275699198054400

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) * H2(k)) * A000142(n) where H2(k) is defined by g.f.: - log(1-x)/(1-x)^2. - 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=2) = sum(k=0, n, n!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k, alpha));
\\ Michel Marcus, Feb 09 2013

Crossrefs

Cf. A000142, A008277.

Sequence in context: A034176 A001765 A246460 * A240404 A093980 A077706

Adjacent sequences: A222142 A222143 A222144 * A222146 A222147 A222148

Keyword

nonn

Author

Michel Marcus, following a suggestion of N. J. A. Sloane , Feb 09 2013

Status

approved