|
|
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
|
|
|
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));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|