Combinatorial triangle !n. This table read by rows gives the coefficients of general sum formulas of n-th left factorials (A003422). The k-th row (k>=1) contains T(i,k) for i=1 to 2*k and k=1 to n-2, where T(i,k) satisfies !n = n + Sum_{k=1..n-2} Sum_{i=1..2*k} T(i,k) * C(n-k-1,i).
A102639
Combinatorial triangle !n. This table read by rows gives the coefficients of general sum formulas of n-th left factorials (A003422). The k-th row (k>=1) contains T(i,k) for i=1 to 2*k and k=1 to n-2, where T(i,k) satisfies !n = n + Sum_{k=1..n-2} Sum_{i=1..2*k} T(i,k) * C(n-k-1,i).
Terms
- a(0) =1a(1) =1a(2) =3a(3) =8a(4) =8a(5) =3a(6) =9a(7) =46a(8) =101a(9) =114a(10) =65a(11) =15a(12) =33a(13) =272a(14) =975a(15) =1935a(16) =2289a(17) =1615a(18) =630a(19) =105a(20) =153a(21) =1796a(22) =9175a(23) =26795a(24) =49474a(25) =60080a(26) =48104a(27) =24535a(28) =7245a(29) =945
External references
- oeis: A102639