A102735 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).

2, 1, 8, 13, 10, 3, 22, 74, 134, 134, 70, 15, 52, 314, 1024, 1964, 2296, 1615, 630, 105, 114, 1155, 6084, 18954, 37512, 48677, 41426, 22330, 6930, 945, 240, 3927, 31494, 146907, 438948, 885653, 1237958, 1204525, 802648, 349965, 90090, 10395, 494

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..43.

Example

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)
= 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
+ 24 + 39 + 10 + 44 + 74 + 52 = 279.

Crossrefs

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

Sequence in context: A214279 A360608 A151501 * A088960 A263528 A121360

Adjacent sequences: A102732 A102733 A102734 * A102736 A102737 A102738

Keyword

nonn,tabl

Author

André F. Labossière, Feb 07 2005

Status

approved