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A101100
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The first summation of row 5 of Euler's triangle - a row that will recursively accumulate to the power of 5.
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4
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1, 27, 93, 119, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| 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.
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FORMULA
| a(x) = Sum [Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; n = 5, r = -5, or a(x) = 120; x>4, or a(k) = Sum[(-1)^j*Binomial[n + 1 - z, j]*(k - j + 1)^n, {j, 0, k + 1}]; n = 5, z = 1, or a(k) = 120; k>3
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MATHEMATICA
| MagicNKZ=Sum[(-1)^j*Binomial[n+1-z, j]*(k-j+1)^n, {j, 0, k+1}]; Table[MagicNKZ, {n, 5, 5}, {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, 5, 5}, {r, -5, -5}, {x, 5, 35}]
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CROSSREFS
| Within the "cube" of related sequences with construction based upon MaginNKZ formula, with n downward, k rightward and z backward . . . Before: this_sequence, A101095, A101096, A101098, A022521, A000584, A000539, A101092, A101099 Above: A101104, this_sequence Within the "cube" of related sequences with construction based upon SeriesAtLevelR formula, with n downward, x rightward and r backward . . . Before: this_sequence, A101095, A101096, A101098, A022521, A000584, A000539, A101092, A101099.
Sequence in context: A043434 A044214 A044595 * A078183 A072252 A154041
Adjacent sequences: A101097 A101098 A101099 * A101101 A101102 A101103
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KEYWORD
| easy,nonn,uned
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AUTHOR
| Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
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