login
Table read by rows giving the coefficients of general sum formulas of n-th sums of Bell numbers (A005001). The k-th row (k>=1) contains T(i,k) for i=1 to 2*k and k=1 to n-3, where T(i,k) satisfies Sum_{q=1..n} Bell(q) = 1 + C(n,2) + Sum_{k=1..n-3} Sum_{i=1..2*k} T(i,k) * C(n-k-2,1).
1

%I #6 Jun 16 2016 23:27:27

%S 2,1,8,13,10,3,22,74,134,134,70,15,52,314,1024,1964,2296,1615,630,105,

%T 114,1155,6084,18954,37512,48677,41426,22330,6930,945,240,3927,31494,

%U 146907,438948,885653,1237958,1204525,802648,349965,90090,10395,494

%N Table read by rows giving the coefficients of general sum formulas of n-th sums of Bell numbers (A005001). The k-th row (k>=1) contains T(i,k) for i=1 to 2*k and k=1 to n-3, where T(i,k) satisfies Sum_{q=1..n} Bell(q) = 1 + C(n,2) + Sum_{k=1..n-3} Sum_{i=1..2*k} T(i,k) * C(n-k-2,1).

%C The coefficients T(i,k) along the i-th columns of the triangle are the consecutive partial sums of those found in table A094262.

%e Sum_Bell(7) = 1 + C(7,2) + 2*C(7-3,1) + C(7-3,2) + ... + 74*C(7-5,2) + 52*C(7-6,1)

%e = 1 + 21 + 8 + 6 + 8*C(3,1) + 13*C(3,2) + 10*C(3,3) + 22*C(2,1) + 74 + 52 = 1 + 21 + 8 + 6

%e + 24 + 39 + 10 + 44 + 74 + 52 = 279.

%Y Cf. A094262, A005001, A000110, A008277, A003422, A000166, A000204, A000045, A000108.

%K nonn,tabl

%O 1,1

%A _André F. Labossière_, Feb 07 2005