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Search: id:A137394
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| A137394 |
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Triangular sequence from a Pidduck polynomials expansion: p(t) = (t/(1 - t))*((1 + t)/(1 - t))^x. |
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+0
1
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| 1, 2, 4, 6, 12, 12, 24, 64, 48, 32, 120, 320, 400, 160, 80, 720, 2208, 2400, 1920, 480, 192, 5040, 15456, 21952, 13440, 7840, 1344, 448, 40320, 135168, 175616, 157696, 62720, 28672, 3584, 1024, 362880, 1216512, 1884672, 1419264, 919296, 258048
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are: {0, 1, 6, 30, 168, 1080, 7920, 65520, 604800, 6168960, 68947200};
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REFERENCES
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Weisstein, Eric W. "Pidduck Polynomial." >http://mathworld.wolfram.com/PidduckPolynomial.html
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FORMULA
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p(t) = (t/(1 - t))*((1 + t)/(1 - t))^x=Sum(s(x,k)*t^k/k!,{k,0,Infinity}]; Out(n,m)=2^(n+2)*n!*Coefficient(s(x,n))
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EXAMPLE
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{0},
{1},
{2, 4},
{6, 12, 12},
{24, 64, 48, 32},
{120, 320, 400, 160, 80},
{720, 2208, 2400, 1920, 480, 192},
{5040, 15456, 21952, 13440, 7840, 1344, 448},
{40320, 135168, 175616, 157696, 62720, 28672, 3584, 1024},
{362880, 1216512, 1884672, 1419264, 919296, 258048, 96768, 9216, 2304}, {3628800, 12971520, 18846720, 18380800, 9192960, 4623360, 967680, 307200, 23040, 5120}
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MATHEMATICA
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Clear[p] p[t_] = (t/(1 - t))*((1 + t)/(1 - t))^x Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A137391 A137392 A137393 this_sequence A137395 A137396 A137397
Sequence in context: A076868 A056793 A137387 this_sequence A062856 A056371 A015733
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KEYWORD
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nonn,uned,tabf
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 10 2008
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