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%I #12 Jun 16 2016 23:27:21
%S 1,1,1,2,1,1,4,3,1,1,10,6,4,1,1,26,18,8,5,1,1,76,48,28,10,6,1,1,232,
%T 156,76,40,12,7,1,1,764,492,272,110,54,14,8,1,1,2620,1740,880,430,150,
%U 70,16,9,1,1,9496,6168,3328,1420,636,196,88,18,10,1,1,35696,23568
%N Triangle read by rows where T(n+1,k)=T(n,k)+n*T(n-1,k) starting with T(n,n)=1 and T(n,k)=0 if n<k.
%C For n>k+1, T(n,k) is a multiple of k+2.
%C Eigentriangle of inverse of (-1)^(n-k)*A094587. Row sums are A187044. - _Paul Barry_, Mar 02 2011
%F T(n, k+1)=(T(n, k-1)-T(n-1, k))/k for 0<k<n.
%e Rows start: 1; 1,1; 2,1,1; 4,3,1,1; 10,6,4,1,1; etc.
%e Triangle begins
%e 1,
%e 1, 1,
%e 2, 1, 1,
%e 4, 3, 1, 1,
%e 10, 6, 4, 1, 1,
%e 26, 18, 8, 5, 1, 1,
%e 76, 48, 28, 10, 6, 1, 1,
%e 232, 156, 76, 40, 12, 7, 1, 1
%e Production matrix begins
%e 1, 1,
%e 1, 0, 1,
%e 1, 1, 0, 1,
%e 2, 1, 1, 0, 1,
%e 4, 3, 1, 1, 0, 1,
%e 10, 6, 4, 1, 1, 0, 1,
%e 26, 18, 8, 5, 1, 1, 0, 1,
%e 76, 48, 28, 10, 6, 1, 1, 0, 1,
%e 232, 156, 76, 40, 12, 7, 1, 1, 0, 1
%e Inverse begins
%e 1,
%e -1, 1,
%e -1, -1, 1,
%e 0, -2, -1, 1,
%e 0, 0, -3, -1, 1,
%e 0, 0, 0, -4, -1, 1,
%e 0, 0, 0, 0, -5, -1, 1,
%e 0, 0, 0, 0, 0, -6, -1, 1
%e - _Paul Barry_, Mar 02 2011
%Y Columns include A000085, A000932, A059480. Right hand columns effectively include A000012 (twice), A000027, A005843, A028552. Cf. A062323 for a triangle with similar formulas.
%K easy,nonn,tabl
%O 0,4
%A _Henry Bottomley_, May 23 2002
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