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Search: id:A027474
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| 1, 21, 294, 3430, 36015, 352947, 3294172, 29647548, 259416045, 2219448385, 18643366434, 154231485954, 1259557135291, 10173346092735, 81386768741880, 645668365352248, 5084638377148953, 39779817891812397, 309398583602985310
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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7th binomial transform of (0,0,1,0,0,0,........). Starting at 1, the three-fold convolution of A000420 (powers of 7). - Paul Barry (pbarry(AT)wit.ie), Mar 08 2003
Number of n-permutations (n=3) of 8 objects r, q, u, v, w, z, x, y with repetition allowed, containing exactly two u's. Example: a(1))=21 because we have : uur, uuq, uuw, uuv, uuz, uux, uuy, uru, uqu, uwu, uvu, uzu, uxu, uyu, ruu, quu, wuu, vuu, zuu, xuu, yuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008
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FORMULA
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G.f.: x^2 / (1-7x)^3. Recurrence: a(n) = 21a(n-1) - 147a(n-2) + 343a(n-3), a(0) = a(1) = 0, a(2) = 1. - Paul Barry (pbarry(AT)wit.ie), Mar 08 2003
Numerators of sequence a[ 3, n ] in (a[ i, j ])^3 where a[ i, j ] = Binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.
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MAPLE
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seq(binomial(n+2, 2)*7^n, n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008
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CROSSREFS
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Third column of A027466. Cf. A081136, A081138.
Sequence in context: A025944 A025962 A081137 this_sequence A021864 A020570 A025940
Adjacent sequences: A027471 A027472 A027473 this_sequence A027475 A027476 A027477
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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EXTENSIONS
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Edited by Ralf Stephan, Dec 30 2004
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