A089511 Triangle of integers used to compute column sequences of array A078739 ((2,2)-Stirling2).

1, -1, 3, 1, -6, 6, -1, 27, -108, 100, 1, -36, 216, -400, 225, -1, 135, -2160, 10000, -16875, 9261, 1, -162, 3240, -20000, 50625, -55566, 21952, -1, 567, -27216, 350000, -1771875, 4084101, -4302592, 1679616, 1, -648, 36288, -560000, 3543750, -10890936, 17210368, -13436928

Offset: 2

Author

Wolfdieter Lang, Dec 01 2003

Keywords

• sign
• easy
• tabl

Comments

The k-th column sequence (without leading zeros) of A078739 is for even k: sum(a(k,m)*((m+1)*m)^n,m=1..k-1)/D(k) and for odd k it is: ((k^2-1)/2)*sum(a(k,m)*((m+1)*m)^n,m=1..k-1)/D(k), where D(k) := A089512(k) and n>=0, k>=2.

Examples

			[1]; [ -1,3]; [1,-6,6]; [ -1,27,-108,100]; ...
a(2,1)=A089512(2)*A089275(1,0)*A089278(1,1)/A089500(1)=1*1*1/1=1;
a(3,2)=A089512(3)*A089276(1,0)*A089278(2,2)/A089500(2)=2*1*3/2=3.
a(4,3)=1*(1+18/(4*3))*24/10 =6; a(5,4)= 18*(1+8/(5*4))*2500/630=100.
k=2 column sequence of A078739 is (1*(2*1)^n)/1 = 2^n. k=3: 4*(-1*(2*1)^n + 3*(3*2)^n)/2 (see A016129).
		

Links

• W. Lang, First 10 rows.

Formula

a(n, m) triangle 2<=n, 1<= m <= (n-1), else 0, with a(2*k, m)= D(2*k)*sum(A089275(k, p)/((m+1)*m)^p, p=0..k-1)*A089278(2*k-1, m)/A089500(2*k-1) and a(2*k+1, m)= D(2*k+1)*sum(A089276(k, p)/((m+1)*m)^p, p=0..k-1)*A089278(2*k, m)/A089500(2*k), where D(n) := A089512(n).