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A261642 Triangle, read by rows, where T(n,k) = (k^2 + k)^(n-k) for k=1..n and n>=1.

%I A261642 #7 May 08 2025 19:41:46
%S A261642 1,2,1,4,6,1,8,36,12,1,16,216,144,20,1,32,1296,1728,400,30,1,64,7776,
%T A261642 20736,8000,900,42,1,128,46656,248832,160000,27000,1764,56,1,256,
%U A261642 279936,2985984,3200000,810000,74088,3136,72,1,512,1679616,35831808,64000000,24300000,3111696,175616,5184,90,1
%N A261642 Triangle, read by rows, where T(n,k) = (k^2 + k)^(n-k) for k=1..n and n>=1.
%C A261642 Matrix inverse of triangle P with element P(n,k) = (-1)^(n-k) * (k^2 + k)^(n-k) / (n-k)! forms triangle A103244.
%e A261642 This triangle begins:
%e A261642 1;
%e A261642 2, 1;
%e A261642 4, 6, 1;
%e A261642 8, 36, 12, 1;
%e A261642 16, 216, 144, 20, 1;
%e A261642 32, 1296, 1728, 400, 30, 1;
%e A261642 64, 7776, 20736, 8000, 900, 42, 1;
%e A261642 128, 46656, 248832, 160000, 27000, 1764, 56, 1;
%e A261642 256, 279936, 2985984, 3200000, 810000, 74088, 3136, 72, 1;
%e A261642 512, 1679616, 35831808, 64000000, 24300000, 3111696, 175616, 5184, 90, 1;
%e A261642 1024, 10077696, 429981696, 1280000000, 729000000, 130691232, 9834496, 373248, 8100, 110, 1; ...
%o A261642 (PARI) {T(n, k) = (k^2 + k)^(n-k)}
%o A261642 for(n=1, 10, for(k=1, n, print1(T(n, k), ", ")); print(""))
%Y A261642 Cf. A103244, A261643 (row sums).
%K A261642 nonn,tabl
%O A261642 1,2
%A A261642 _Paul D. Hanna_, Aug 27 2015