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A087111
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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,7). The p-th row (p>=1) contains a(i,p) for i=1 to 7*p-6, where a(i,p) satisfies Sum_{i=1..n} C(i+6,7)^p = 8 * C(n+7,8) * Sum_{i=1..7*p-6} a(i,p) * C(n-1,i-1)/(i+7).
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7
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1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 63, 1169, 10703, 58821, 214123, 545629, 1004307, 1356194, 1347318, 974862, 500346, 172788, 36036, 3432, 1, 511, 45633, 1589567, 29302889, 333924087, 2577462937, 14287393351, 59159005164, 188008120188
(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+8, i-2*k+1)^(p-1) -C(i-1, 2*k-1)*C(i-2*k+7, i-2*k)^(p-1) ]
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EXAMPLE
| Row 3 contains 1,63,1169,...,3432, so Sum_{i=1..n} C(i+6,7)^3 = 8 * C(n+7,8) * [ a(1,3)/8 + a(2,3)*C(n-1,1)/9 + a(3,3)*C(n-1,2)/10 + ... + a(15,3)*C(n-1,14)/22 ] = 8 * C(n+7,8) * [ 1/8 + 63*C(n-1,1)/9 + 1169*C(n-1,2)/10 + ... + 3432*C(n-1,14)/22 ]. Cf. A086030 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, A087110, A000580, A086027, A086028, A027555, A086029, A086030.
Sequence in context: A032639 A015729 A001485 * A173676 A131893 A045849
Adjacent sequences: A087108 A087109 A087110 * A087112 A087113 A087114
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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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