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A348014 Triangle, read by rows, with row n forming the coefficients in Product_{k=0..n} (1 + k^k*x).

%I A348014 #22 Sep 25 2021 06:42:29
%S A348014 1,1,1,1,5,4,1,32,139,108,1,288,8331,35692,27648,1,3413,908331,
%T A348014 26070067,111565148,86400000,1,50069,160145259,42405161203,
%U A348014 1216436611100,5205269945088,4031078400000
%N A348014 Triangle, read by rows, with row n forming the coefficients in Product_{k=0..n} (1 + k^k*x).
%H A348014 Seiichi Manyama, <a href="/A348014/b348014.txt">Rows n = 0..37, flattened</a>
%F A348014 T(0,0) = 1; T(n,k) = T(n-1,k) + n^n * T(n-1,k-1).
%e A348014 Triangle begins:
%e A348014   1;
%e A348014   1,    1;
%e A348014   1,    5,      4;
%e A348014   1,   32,    139,      108;
%e A348014   1,  288,   8331,    35692,     27648;
%e A348014   1, 3413, 908331, 26070067, 111565148, 86400000;
%o A348014 (PARI) T(n, k) = if(k==0, 1, if(k==n, prod(j=1, n, j^j), T(n-1, k)+n^n*T(n-1, k-1)));
%o A348014 (PARI) row(n) = Vecrev(prod(k=1, n, 1+k^k*x));
%Y A348014 Column k=1 gives A001923.
%Y A348014 The diagonal of the triangle is A002109.
%Y A348014 Cf. A007318, A008955, A023531, A108084, A173007, A173008, A249677.
%K A348014 nonn,tabl
%O A348014 0,5
%A A348014 _Seiichi Manyama_, Sep 24 2021