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Search: id:A137478
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| A137478 |
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A triangle of recursive Fibonacci Lah numbers: f(n) = Fibonacci[n]*f(n - 1); L(n, k) = Binomial[n - 1, k - 1]*(f(n)/f(k)). |
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1
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| 1, 1, 1, 2, 4, 1, 6, 18, 9, 1, 30, 120, 90, 20, 1, 240, 1200, 1200, 400, 40, 1, 3120, 18720, 23400, 10400, 1560, 78, 1, 65520, 458640, 687960, 382200, 76440, 5733, 147, 1, 2227680, 17821440, 31187520, 20791680, 5197920, 519792, 19992, 272, 1
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums are:
{1, 2, 7, 34, 261, 3081, 57279, 1676641, 77766297, 5728225636, 671925730146}
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REFERENCES
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Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page86
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FORMULA
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f(n) = Fibonacci[n]*f(n - 1); L(n, k) = Binomial[n - 1, k - 1]*(f(n)/f(k)).
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EXAMPLE
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{1},
{1, 1},
{2, 4, 1},
{6, 18, 9, 1},
{30, 120, 90, 20, 1},
{240, 1200, \
1200, 400, 40, 1},
{3120, 18720, 23400, 10400, 1560, 78, 1},
{65520, 458640, \
687960, 382200, 76440, 5733, 147, 1},
{2227680, 17821440, 31187520, 20791680, 5197920, 519792, 19992, 272, 1},
{122522400, 1102701600, 2205403200, 1715313600, 514594080, 64324260, 3298680, 67320, 495, 1},
{10904493600, 109044936000, 245351106000, 218089872000, 76331455200, 11449718280, 733956300, 19971600, 220275, 890, 1}
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MATHEMATICA
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Clear[f, L] f[0] = 1; f[1] = 1; f[n_] := f[n] = Fibonacci[n]*f[n - 1]; Table[f[n], {n, 1, 10}]; L[n_, k_] := L[n, k] = Binomial[n - 1, k - 1]*(f[n]/f[k]); a = Table[Table[L[n, k], {k, 1, n}], {n, 1, 11}]; Flatten[a] Table[Apply[Plus, Table[L[n, k], {k, 1, n}]], {n, 1, 11}];
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CROSSREFS
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Cf. A000045, A105278.
Sequence in context: A011369 A110877 A021009 this_sequence A089087 A119303 A105552
Adjacent sequences: A137475 A137476 A137477 this_sequence A137479 A137480 A137481
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 22 2008
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