1,2

D. J. Pengelley, The bridge between the continuous and the discrete via original sources in Study the Masters: The Abel-Fauvel Conference [pdf], Kristiansand, 2002, (ed. Otto Bekken et al), National Center for Mathematics Education, University of Gothenburg, Sweden, in press.

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

Eric Weisstein, Link to section of MathWorld: Worpitzky's Identity of 1883.

Eric Weisstein, Link to section of MathWorld: Eulerian Number.

Eric Weisstein, Link to section of MathWorld: Nexus number.

Eric Weisstein, Link to section of MathWorld: Finite Differences.

a(x) = Sum [Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; n = 4, r = -4, or a(x) = 24; x>3, or a(k) = Sum[(-1)^j*Binomial[n + 1 - z, j]*(k - j + 1)^n, {j, 0, k + 1}]; n = 4, z = 1, or a(k) = 24; k>2

MagicNKZ=Sum[(-1)^j*Binomial[n+1-z, j]*(k-j+1)^n, {j, 0, k+1}]; Table[MagicNKZ, {n, 4, 4}, {z, 1, 1}, {k, 0, 34}] OR SeriesAtLevelR = Sum[Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; Table[SeriesAtLevelR, {n, 4, 4}, {r, -4, -4}, {x, 4, 35}]

Within the "cube" of related sequences with construction based upon MaginNKZ formula, with n downward, k rightward and z backward . . . Before: this_sequence, A101103, A005914, A005917, A000583, A000538, A101089, A101090, A101091 Above: A101101, this_sequence, Below: A101100 Within the "cube" of related sequences with construction based upon SeriesAtLevelR formula, with n downward, x rightward and r backward . . . Before: this_sequence, A101103, A005914, A005917, A000583, A000538, A101089, A101090, A101091 Above: this_sequence, Below: A101095.

Sequence in context: A115703 A014633 A066458 this_sequence A114455 A048992 A088783

Adjacent sequences: A101101 A101102 A101103 this_sequence A101105 A101106 A101107

easy,nonn,uned

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004