This table shows the coefficients of combinatorial formulas 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).
A087107
This table shows the coefficients of combinatorial formulas 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).
Terms
- a(0) =1a(1) =1a(2) =3a(3) =3a(4) =1a(5) =1a(6) =15a(7) =69a(8) =147a(9) =162a(10) =90a(11) =20a(12) =1a(13) =63a(14) =873a(15) =5191a(16) =16620a(17) =31560a(18) =36750a(19) =25830a(20) =10080a(21) =1680a(22) =1a(23) =255a(24) =9489a(25) =130767a(26) =919602a(27) =3832650a(28) =10238000a(29) =18244380
External references
- oeis: A087107