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A222145 a(n) = n-th second-order hyperharmonic-exponential number, multiplied by n!. 0
0, 1, 7, 77, 1222, 26364, 739608, 26079780, 1125791280, 58257484128, 3552890064480, 251777905728480, 20488109614761600, 1895120214639868800, 197527783071095930880, 23023412842885582176000, 2980946191374310495795200, 426192103002275699198054400 (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) * 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

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

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Last modified January 29 14:07 EST 2020. Contains 331338 sequences. (Running on oeis4.)