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A269957 Triangle read by rows, T(n,k) = Sum_{j=k..n} A269940(n,j)*A269939(j,k), for n>=0 and 0<=k<=n.

%I A269957 #10 Mar 14 2020 16:36:23
%S A269957 1,0,1,0,5,9,0,41,210,225,0,469,5115,14175,11025,0,6889,142492,763350,
%T A269957 1455300,893025,0,123605,4566149,41943090,146522250,212837625,
%U A269957 108056025,0,2620169,166939742,2462128095,13973628900,35936814375,42141849750,18261468225
%N A269957 Triangle read by rows, T(n,k) = Sum_{j=k..n} A269940(n,j)*A269939(j,k), for n>=0 and 0<=k<=n.
%F A269957 T(n,n) = A001818(n).
%F A269957 T(n,1) = A032188(n+1) for n>=1.
%e A269957 Triangle starts:
%e A269957 [1]
%e A269957 [0, 1]
%e A269957 [0, 5, 9]
%e A269957 [0, 41, 210, 225]
%e A269957 [0, 469, 5115, 14175, 11025]
%e A269957 [0, 6889, 142492, 763350, 1455300, 893025]
%o A269957 (Sage)
%o A269957 F = lambda n,k,f: sum((-1)^(m+k)*binomial(n+k,n+m)*f(n+m,m) for m in (0..k))
%o A269957 T = lambda n,k: sum(F(n, j, stirling_number1)*F(j, k, stirling_number2) for j in (k..n))
%o A269957 for n in (0..6): print([T(n, k) for k in (0..n)])
%Y A269957 Cf. A001818, A032188, A269939, A269940.
%K A269957 nonn,tabl
%O A269957 0,5
%A A269957 _Peter Luschny_, Mar 27 2016