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A163204 Triangle read by rows, A095989 convolved with A000670.

%I A163204 #13 Dec 10 2016 12:32:40
%S A163204 1,1,2,3,2,8,13,6,8,48,75,26,24,48,368,541,150,104,144,368,3376,4683,
%T A163204 1082,600,624,1104,3376,35824,47293,9366,4328,3600,4784,10128,35824,
%U A163204 430512,545835,94586,37464,25968,27600,43888,107472,430512,5773936,7087261,1091670,378344,224784,199088,253200,465712,1291536,5773936,85482032
%N A163204 Triangle read by rows, A095989 convolved with A000670.
%C A163204 Row sums = A000670 starting with offset 1: (1, 3, 13, 75, 541, 4683,...).
%C A163204 Left border = A000670, right border = A095989.
%C A163204 Second column: A076726. - _Michel Marcus_, Mar 31 2016
%H A163204 G. C. Greubel, <a href="/A163204/b163204.txt">Table of n, a(n) for n = 1..1225</a>
%F A163204 Descending antidiagonals of a multiplication table formed by convolving A095989 with A000670, where A095989 is the INVERTi transform of A000670 starting (1, 3, 13, 75,...).
%e A163204 First few rows of the triangle are:
%e A163204 1;
%e A163204 1, 2;
%e A163204 3, 2, 8;
%e A163204 13, 6, 8, 48;
%e A163204 75, 26, 24, 48, 368;
%e A163204 541, 150, 104, 144, 368, 3376;
%e A163204 4683, 1082, 600, 624, 1104, 3376, 35824;
%e A163204 47293, 9366, 4328, 3600, 4784, 10128, 35824, 430512;
%e A163204 ...
%t A163204 max = 10; Fubini[n_, r_] := Sum[k!*Sum[(-1)^(i+k+r)*(i+r)^(n-r)/(i!*(k - i - r)!), {i, 0, k - r}], {k, r, n}]; Fubini[0, 1] = 1; A000670 = Table[ Fubini[n, 1], {n, 0, max}]; s = 1 - 1/Sum[Fubini[k, 1] q^k, {k, 0, max}] + O[q]^max; A095989 = CoefficientList[s/q, q]; row[n_] := A095989[[1 ;; n]]*Reverse[A000670[[1 ;; n]]]; Table[row[n], {n, 1, max-1}] // Flatten (* _Jean-François Alcover_, Mar 31 2016 *)
%Y A163204 Cf. A000670, A076726, A095989.
%K A163204 nonn,tabl
%O A163204 1,3
%A A163204 _Gary W. Adamson_, Jul 23 2009
%E A163204 a(23) corrected by _Jean-François Alcover_, Mar 31 2016
%E A163204 Terms a(37) onward added by _G. C. Greubel_, Dec 10 2016