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A101104
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The first summation of row 4 of Euler's triangle - a row that will recursively accumulate to the power of 4.
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5
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1, 12, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24
(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 = 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
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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, 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}]
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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, 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 * A114455 A048992 A088783
Adjacent sequences: A101101 A101102 A101103 * A101105 A101106 A101107
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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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