This table shows the coefficients of combinatorial formulas 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).
A087111
This table shows the coefficients of combinatorial formulas 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).
Terms
- a(0) =1a(1) =1a(2) =7a(3) =21a(4) =35a(5) =35a(6) =21a(7) =7a(8) =1a(9) =1a(10) =63a(11) =1169a(12) =10703a(13) =58821a(14) =214123a(15) =545629a(16) =1004307a(17) =1356194a(18) =1347318a(19) =974862a(20) =500346a(21) =172788a(22) =36036a(23) =3432a(24) =1a(25) =511a(26) =45633a(27) =1589567a(28) =29302889a(29) =333924087
External references
- oeis: A087111