This table shows the coefficients of combinatorial formulas 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).
A087110
This table shows the coefficients of combinatorial formulas 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).
Terms
- a(0) =1a(1) =1a(2) =6a(3) =15a(4) =20a(5) =15a(6) =6a(7) =1a(8) =1a(9) =48a(10) =687a(11) =4850a(12) =20385a(13) =55908a(14) =104959a(15) =137886a(16) =127050a(17) =80640a(18) =33642a(19) =8316a(20) =924a(21) =1a(22) =342a(23) =21267a(24) =527876a(25) =7020525a(26) =58015362a(27) =324610399a(28) =1297791264a(29) =3839203452
External references
- oeis: A087110