A119687 f-Pascal's triangle where f(n) = n^2 = A000290(n).

1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 26, 50, 26, 1, 1, 677, 3176, 3176, 677, 1, 1, 458330, 10545305, 20173952, 10545305, 458330, 1, 1, 210066388901, 111413523931925, 518191796841329, 518191796841329, 111413523931925, 210066388901, 1

Offset: 0

Author

Philippe Deléham, Jun 09 2006

Keywords

• nonn
• tabl

Comments

The second diagonal, T(n,n-1) = A003095(n). - Cortney Reagle, Sep 17 2019

Examples

			Triangle T(n,k) (with rows n >= 0 and columns 0 <= k <= n) begins as follows:
  1;
  1,      1;
  1,      2,        1;
  1,      5,        5,        1;
  1,     26,       50,       26,        1;
  1,    677,     3176,     3176,      677,      1;
  1, 458330, 10545305, 20173952, 10545305, 458330, 1;
  ...
		

Links

• Cortney Reagle, Table of n, a(n) for n = 0..104 (Rows n = 0..12 of the triangle, flattened)

Crossrefs

Row sums are A327563.

Cf. A007318, A003095.

Programs

PARI

T(n)={my(M=matrix(n,n)); M[1,1]=1; for(n=2, n, M[n,1]=1; for(k=2, n, M[n,k]=M[n-1,k-1]^2 + M[n-1,k]^2)); M}
{ my(A=T(7)); for(i=1, #A, print(A[i,1..i])) } \\ Andrew Howroyd, Sep 17 2019

Formula

T(n, k) = T(n-1, k-1)^2 + T(n-1, k)^2; T(0,0) = 1; T(n,-1) = 0; T(n, k) = 0, n < k.

Extensions

a(12) = 50 inserted and more terms added by Cortney Reagle, Sep 17 2019