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A176276 Worpitzky(n, k)*Harmonic(k), triangle read by rows. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A134813 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

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)