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A375577 Array read by ascending antidiagonals: A(n,k) = k^n + k*n + 1.

%I A375577 #8 Aug 25 2024 18:49:16
%S A375577 2,1,2,1,3,2,1,4,5,2,1,5,9,7,2,1,6,15,16,9,2,1,7,25,37,25,11,2,1,8,43,
%T A375577 94,77,36,13,2,1,9,77,259,273,141,49,15,2,1,10,143,748,1045,646,235,
%U A375577 64,17,2,1,11,273,2209,4121,3151,1321,365,81,19,2
%N A375577 Array read by ascending antidiagonals: A(n,k) = k^n + k*n + 1.
%F A375577 G.f. for the k-th column: (2*x^2 - 3*x - k^2 + k + 1)/((x - 1)^2*(x - k)).
%F A375577 E.g.f. for the k-th column: exp(x)*(1 + exp((k-1)*x) + k*x).
%F A375577 A(n,1) = n + 2.
%F A375577 A(2,n) = A000290(n+1).
%F A375577 A(n,n) = 2*A214647(n) + 1.
%e A375577 Array begins:
%e A375577   2, 2,  2,   2,    2,     2, ...
%e A375577   1, 3,  5,   7,    9,    11, ...
%e A375577   1, 4,  9,  16,   25,    36, ...
%e A375577   1, 5, 15,  37,   77,   141, ...
%e A375577   1, 6, 25,  94,  273,   646, ...
%e A375577   1, 7, 43, 259, 1045,  3151, ...
%e A375577   1, 8, 77, 748, 4121, 15656, ...
%e A375577   ...
%t A375577 A[0,0]=2; A[n_,k_]:=k^n+k*n+1;Table[A[n-k,k],{n,0,10},{k,0,n}]//Flatten
%Y A375577 Cf. A000290, A004247, A004248, A005408 (n=1), A005491 (n=3), A007395 (n=0), A054977 (k=0), A176691 (k=2), A176805 (k=3), A176916 (k=5), A176972 (k=7), A214647.
%Y A375577 Cf. A375578 (antidiagonal sums).
%K A375577 nonn,easy,tabl
%O A375577 0,1
%A A375577 _Stefano Spezia_, Aug 19 2024