A176276 Worpitzky(n, k)*Harmonic(k), triangle read by rows.

0, 0, 1, 0, 3, 3, 0, 7, 18, 11, 0, 15, 75, 110, 50, 0, 31, 270, 715, 750, 274, 0, 63, 903, 3850, 7000, 5754, 1764, 0, 127, 2898, 18711, 52500, 72884, 49392, 13068, 0, 255, 9075, 85470, 347550, 725004, 814968, 470448, 109584, 0, 511, 27990, 375155, 2126250, 6254598, 10372320, 9801000, 4931280, 1026576

Offset

0,5

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Peter Luschny, A sequence transformation and the Bernoulli numbers.

Formula

T(n, k) = abs(Stirling1(k+1, 2) * Stirling2(n+1, k+1)).

Example

Triangle begins as:
  0;
  0,  1;
  0,  3,   3;
  0,  7,  18,  11;
  0, 15,  75, 110,  50;
  0, 31, 270, 715, 750, 274;

Maple

T176276 := proc(n, k) local W, H;
W := proc(n, k) stirling2(n+1, k+1)*k! end:
H := proc(n) local i; add(1/i, i=1..n) end: # H(0) = 0 (empty sum convention)
W(n, k)*H(k) end:

Mathematica

T[n_, k_]:= StirlingS2[n+1, k+1]*k!*HarmonicNumber[k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* Jean-François Alcover, Jul 29 2013 *)

Prog

(PARI) T(n, k) = k!*stirling(n+1, k+1, 2)*sum(j=1, k, 1/j); \\ G. C. Greubel, Nov 24 2019
(Magma) [Abs(StirlingFirst(k+1, 2)*StirlingSecond(n+1, k+1)): k in [0..n], n in [0..10]];
(Sage) [[factorial(k)*stirling_number1(n+1, k+1)*harmonic_number(k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 24 2019
(GAP) Flat(List([0..10], n-> List([0..n], k-> AbsInt(Stirling1(k+1, 2) * Stirling2(n+1, k+1)) ))); # G. C. Greubel, Nov 24 2019

Crossrefs

Cf. A028246, A176277.

Sequence in context: A338037 A164107 A093755 * A200701 A275408 A169670

Adjacent sequences: A176273 A176274 A176275 * A176277 A176278 A176279

Keyword

easy,nonn,tabl

Author

Peter Luschny, Apr 14 2010

Status

approved