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A087107
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This table shows the sobalian coefficients of combinatorial formulae needed for generating the sequential sums of p-th powers of tetrahedral numbers. The p-th row (p>=1) contains a(i,p) for i=1 to 3*p-2, where a(i,p) satisfies Sum_{i=1..n} C(i+2,3)^p = 4 * C(n+3,4) * Sum_{i=1..3*p-2} a(i,p) * C(n-1,i-1)/(i+3).
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7
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1, 1, 3, 3, 1, 1, 15, 69, 147, 162, 90, 20, 1, 63, 873, 5191, 16620, 31560, 36750, 25830, 10080, 1680, 1, 255, 9489, 130767, 919602, 3832650, 10238000, 18244380, 21990360, 17745000, 9198000, 2772000, 369600, 1, 1023, 97953, 2903071, 40317780
(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+4, i-2*k+1)^(p-1) -C(i-1, 2*k-1)*C(i-2*k+3, i-2*k)^(p-1) ]
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EXAMPLE
| Row 3 contains 1,15,69,147,162,90,20, so Sum_{i=1..n} C(i+2,3)^3 = 4 * C(n+3,4) * [ a(1,3)/4 + a(2,3)*C(n-1,1)/5 + a(3,3)*C(n-1,2)/6 + ... + a(7,3)*C(n-1,6)/10 ] = 4 * C(n+3,4) * [ 1/4 + 15*C(n-1,1)/5 + 69*C(n-1,2)/6 + 147*C(n-1,3)/7 + 162*C(n-1,4)/8 + 90*C(n-1,5)/9 + 20*C(n-1,6)/10 ]. Cf. A086021 for more details.
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CROSSREFS
| Cf. A000292, A024166, A087127, A024166, A085438, A085439, A085440, A085441, A085442, A000332, A086020, A086021, A086022, A087108, A000389, A086023, A086024, A087109, A000579, A086025, A086026, A087110, A000580, A086027, A086028, A087111, A027555, A086029, A086030.
Sequence in context: A176344 A075837 A178885 * A155170 A126460 A173503
Adjacent sequences: A087104 A087105 A087106 * A087108 A087109 A087110
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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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