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A222061
Triangle read by rows: coefficients of second-order hypergeometric-harmonic polynomials.
1
0, 0, 1, 0, 1, 5, 0, 1, 15, 26, 0, 1, 35, 156, 154, 0, 1, 75, 650, 1540, 1044, 0, 1, 155, 2340, 10010, 15660, 8028, 0, 1, 315, 7826, 53900, 146160, 168588, 69264, 0, 1, 635, 25116, 261954, 1096200, 2135448, 1939392, 663696, 0, 1, 1275, 78650, 1196580, 7256844
OFFSET
0,6
FORMULA
T(n,k) = A008277(n,k)*A000142(k)*H2(k) where H2(k) is defined by g.f.:- log(1-x)/(1-x)^2. - Michel Marcus, Feb 09 2013
EXAMPLE
Triangle begins:
0
0 1
0 1 5
0 1 15 26
0 1 35 156 154
0 1 75 650 1540 1044
....
MATHEMATICA
H2[k_] := (k+1) (HarmonicNumber[k+1] - 1);
T[n_, k_] := StirlingS2[n, k] k! H2[k];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 01 2018 *)
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, 2)};
\\ Michel Marcus, Feb 09 2013
CROSSREFS
Cf. A222057-A222064. Row sums are in A222062.
Sequence in context: A241855 A221800 A291774 * A345453 A064315 A371994
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Feb 08 2013
EXTENSIONS
More terms from Michel Marcus, Feb 09 2013
STATUS
approved