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A222063
Triangle read by rows: coefficients of third-order hypergeometric-harmonic polynomials.
1
0, 0, 1, 0, 1, 7, 0, 1, 21, 47, 0, 1, 49, 282, 342, 0, 1, 105, 1175, 3420, 2754, 0, 1, 217, 4230, 22230, 41310, 24552, 0, 1, 441, 14147, 119700, 385560, 515592, 241128, 0, 1, 889, 45402, 581742, 2891700, 6530832, 6751584, 2592720, 0, 1, 1785, 142175, 2657340
OFFSET
0,6
FORMULA
T(n,k) = 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
EXAMPLE
Triangle begins:
0
0 1
0 1 7
0 1 21 47
0 1 49 282 342
0 1 105 1175 3420 2754
....
PROG
(PARI)
hyp(n, alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y); }
t(n, k) = {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 give A222064.
Sequence in context: A153626 A297787 A101031 * A156960 A287697 A335953
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Feb 08 2013
EXTENSIONS
More terms from Michel Marcus, Feb 09 2013
STATUS
approved