A222063 Triangle read by rows: coefficients of third-order hypergeometric-harmonic polynomials.

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

Links

Table of n, a(n) for n=0..49.

Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.

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

Adjacent sequences: A222060 A222061 A222062 * A222064 A222065 A222066

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 08 2013

Extensions

More terms from Michel Marcus, Feb 09 2013

Status

approved