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A087110
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This table shows the sobalian coefficients of combinatorial formulae needed for generating the sequential sums of p-th powers of binomial coefficients C(n,6). The p-th row (p>=1) contains a(i,p) for i=1 to 6*p-5, where a(i,p) satisfies Sum_{i=1..n} C(i+5,6)^p = 7 * C(n+6,7) * Sum_{i=1..6*p-5} a(i,p) * C(n-1,i-1)/(i+6).
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6
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1, 1, 6, 15, 20, 15, 6, 1, 1, 48, 687, 4850, 20385, 55908, 104959, 137886, 127050, 80640, 33642, 8316, 924, 1, 342, 21267, 527876, 7020525, 58015362, 324610399, 1297791264, 3839203452, 8595153000, 14760228672, 19560928464, 19987430694
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(i, p) = Sum_{k=1..[2*i+1+(-1)^(i-1)]/4} [ C(i-1, 2*k-2)*C(i-2*k+7, i-2*k+1)^(p-1) -C(i-1, 2*k-1)*C(i-2*k+6, i-2*k)^(p-1) ]
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EXAMPLE
| Row 3 contains 1,48,687,...,924, so Sum_{i=1..n} C(i+5,6)^3 = 7 * C(n+6,7) * [ a(1,3)/7 + a(2,3)*C(n-1,1)/8 + a(3,3)*C(n-1,2)/9 + ... + a(13,3)*C(n-1,12)/19 ] = 7 * C(n+6,7) * [ 1/7 + 48*C(n-1,1)/8 + 687*C(n-1,2)/9 + ... + 924*C(n-1,12)/19 ]. Cf. A086028 for more details.
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CROSSREFS
| Cf. A000292, A024166, A087127, A024166, A085438, A085439, A085440, A085441, A085442, A087107, A000332, A086020, A086021, A086022, A087108, A000389, A086023, A086024, A087109, A000579, A086025, A086026, A000580, A086027, A086028, A087111, A027555, A086029, A086030.
Sequence in context: A001484 A173680 A176849 * A063266 A131892 A045848
Adjacent sequences: A087107 A087108 A087109 * A087111 A087112 A087113
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Andre F. Labossiere (boronali(AT)laposte.net), Aug 11 2003
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 16 2003
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