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

%I A089511 #10 Aug 29 2019 17:22:51
%S A089511 1,-1,3,1,-6,6,-1,27,-108,100,1,-36,216,-400,225,-1,135,-2160,10000,
%T A089511 -16875,9261,1,-162,3240,-20000,50625,-55566,21952,-1,567,-27216,
%U A089511 350000,-1771875,4084101,-4302592,1679616,1,-648,36288,-560000,3543750,-10890936,17210368,-13436928
%N A089511 Triangle of integers used to compute column sequences of array A078739 ((2,2)-Stirling2).
%C A089511 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.
%H A089511 W. Lang, <a href="/A089511/a089511.txt">First 10 rows</a>.
%F A089511 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).
%e A089511 [1]; [ -1,3]; [1,-6,6]; [ -1,27,-108,100]; ...
%e A089511 a(2,1)=A089512(2)*A089275(1,0)*A089278(1,1)/A089500(1)=1*1*1/1=1;
%e A089511 a(3,2)=A089512(3)*A089276(1,0)*A089278(2,2)/A089500(2)=2*1*3/2=3.
%e A089511 a(4,3)=1*(1+18/(4*3))*24/10 =6; a(5,4)= 18*(1+8/(5*4))*2500/630=100.
%e A089511 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).
%K A089511 sign,easy,tabl
%O A089511 2,3
%A A089511 _Wolfdieter Lang_, Dec 01 2003