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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 (list; table; graph; refs; listen; history; text; internal format)
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 A067840

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

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Last modified July 15 02:26 EDT 2020. Contains 335762 sequences. (Running on oeis4.)