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%I #24 Sep 23 2015 15:26:27
%S 1,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%T 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U 6,6,6,6,6,6,6,6,6,6,6,6
%N a(1)=1, a(2)=5, and a(n)=6 for n>=3.
%C Previous name was: The first summation of row 3 of Euler's triangle - a row that will recursively accumulate to the power of 3.
%H D. J. Pengelley, <a href="http://www.math.nmsu.edu/~davidp/bridge.pdf">The bridge between the continuous and the discrete via original sources in Study the Masters: The Abel-Fauvel Conference</a> [pdf], Kristiansand, 2002, (ed. Otto Bekken et al.), National Center for Mathematics Education, University of Gothenburg, Sweden, in press.
%H C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>. [broken link: domain now owned by a domain grabber]
%H Eric Weisstein, Link to section of MathWorld: <a href="http://mathworld.wolfram.com/WorpitzkysIdentity.html">Worpitzky's Identity of 1883</a>.
%H Eric Weisstein, Link to section of MathWorld: <a href="http://mathworld.wolfram.com/EulerianNumber.html">Eulerian Number</a>.
%H Eric Weisstein, Link to section of MathWorld: <a href="http://mathworld.wolfram.com/NexusNumber.html">Nexus number</a>.
%H Eric Weisstein, Link to section of MathWorld: <a href="http://mathworld.wolfram.com/FiniteDifference.html">Finite Differences</a>.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F G.f.: x*(1+4*x+x^2)/(1-x). - _L. Edson Jeffery_, Jan 29 2012
%t MagicNKZ=Sum[(-1)^j*Binomial[n+1-z, j]*(k-j+1)^n, {j, 0, k+1}];Table[MagicNKZ, {n, 3, 3}, {z, 1, 1}, {k, 0, 34}] (* OR *)
%t SeriesAtLevelR = Sum[Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; Table[SeriesAtLevelR, {n, 3, 3}, {r, -3, -3}, {x, 4, 35}]
%t Join[{1, 5},LinearRecurrence[{1},{6},78]] (* _Ray Chandler_, Sep 23 2015 *)
%Y Within the "cube" of related sequences with construction based upon MaginNKZ formula, with n downward, k rightward and z backward:
%Y Before: this_sequence, A008458, A003215, A000578, A000537, A024166 or A024166, A101094, A101097, A101102.
%Y Above: this_sequence, below: A101104, A101100.
%Y Within the "cube" of related sequences with construction based upon SeriesAtLevelR formula, with n downward, x rightward and r backward:
%Y Above: this_sequence, below: A101103, A101096.
%K easy,nonn,uned
%O 1,2
%A Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
%E I wish the sequence was as interesting as the list of references! - _N. J. A. Sloane_
%E New name from _Joerg Arndt_, Nov 30 2014
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