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

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, 94, 77, 36, 13, 2, 1, 9, 77, 259, 273, 141, 49, 15, 2, 1, 10, 143, 748, 1045, 646, 235, 64, 17, 2, 1, 11, 273, 2209, 4121, 3151, 1321, 365, 81, 19, 2

Offset: 0

Author

Stefano Spezia, Aug 19 2024

Keywords

• nonn
• easy
• tabl

Examples

			Array begins:
  2, 2,  2,   2,    2,     2, ...
  1, 3,  5,   7,    9,    11, ...
  1, 4,  9,  16,   25,    36, ...
  1, 5, 15,  37,   77,   141, ...
  1, 6, 25,  94,  273,   646, ...
  1, 7, 43, 259, 1045,  3151, ...
  1, 8, 77, 748, 4121, 15656, ...
  ...
		

Crossrefs

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.

Cf. A375578 (antidiagonal sums).

Programs

Mathematica

A[0,0]=2; A[n_,k_]:=k^n+k*n+1;Table[A[n-k,k],{n,0,10},{k,0,n}]//Flatten

Formula

G.f. for the k-th column: (2*x^2 - 3*x - k^2 + k + 1)/((x - 1)^2*(x - k)).

E.g.f. for the k-th column: exp(x)*(1 + exp((k-1)*x) + k*x).

A(n,1) = n + 2.

A(2,n) = A000290(n+1).

A(n,n) = 2*A214647(n) + 1.