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%I #14 Dec 07 2019 08:14:46
%S 1,2,1,5,4,1,15,14,7,1,52,51,36,11,1,203,202,171,81,16,1,877,876,813,
%T 512,162,22,1,4140,4139,4012,3046,1345,295,29,1,21147,21146,20891,
%U 17866,10096,3145,499,37,1,115975,115974,115463
%N Triangle read by rows, A008277 * A000012.
%C Left column = Bell numbers (A000110) starting (1, 2, 5, 15, 52, 203, ...). Row sums = A005493(n+1): (1, 3, 10, 37, 151, 674, ...).
%C Corresponding to the generalized Stirling number triangle of first kind A049444. - _Peter Luschny_, Sep 18 2011
%F A008277 * A000012 as infinite lower triangular matrices. Partial sums of A008277 rows starting from the right.
%e First few rows of the triangle are
%e 1;
%e 2, 1;
%e 5, 4, 1;
%e 15, 14, 7, 1;
%e 52, 51, 36, 11, 1;
%e 203, 202, 171, 81, 16, 1;
%e 877, 876, 813, 512, 162, 22, 1;
%e ...
%p A137650_row := proc(n) local k,i;
%p add(add(combinat[stirling2](n, n-i), i=0..k)*x^(n-k-1),k=0..n-1);
%p seq(coeff(%,x,k),k=0..n-1) end:
%p seq(print(A137650_row(n)),n=1..7); # _Peter Luschny_, Sep 18 2011
%t row[n_] := Table[StirlingS2[n, k], {k, 0, n}] // Reverse // Accumulate // Reverse // Rest;
%t Array[row, 10] // Flatten (* _Jean-François Alcover_, Dec 07 2019 *)
%Y Cf. A000110, A008277, A005493, A049444.
%Y A similar triangle is A133611.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Feb 01 2008
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