A222061 Triangle read by rows: coefficients of second-order hypergeometric-harmonic polynomials.

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

Links

Table of n, a(n) for n=0..50.

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)*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

Adjacent sequences: A222058 A222059 A222060 * A222062 A222063 A222064

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 08 2013

Extensions

More terms from Michel Marcus, Feb 09 2013

Status

approved