A107415 -id:A107415 - cp's OEIS frontend

A249677 Triangle, read by rows, with row n forming the coefficients in Product_{k=0..n} (1 + k^3*x).

1, 1, 1, 1, 9, 8, 1, 36, 251, 216, 1, 100, 2555, 16280, 13824, 1, 225, 15055, 335655, 2048824, 1728000, 1, 441, 63655, 3587535, 74550304, 444273984, 373248000, 1, 784, 214918, 25421200, 1305074809, 26015028256, 152759224512, 128024064000, 1, 1296, 616326, 135459216, 14320729209, 694213330464, 13472453691584, 78340747014144, 65548320768000

Offset: 0

Paul D. Hanna, Nov 03 2014

Column 1 forms the squares of the triangular numbers (A000537).
Main diagonal forms the cubes of the factorial numbers (A000442).
Row sums equal Product_{k=1..n} (k^3 + 1) = n!*Product_{k=1..n} (k*(k-1) + 1) = n!*A130032(n).

			Triangle begins:
  1;
  1, 1;
  1, 9, 8;
  1, 36, 251, 216;
  1, 100, 2555, 16280, 13824;
  1, 225, 15055, 335655, 2048824, 1728000;
  1, 441, 63655, 3587535, 74550304, 444273984, 373248000;
  1, 784, 214918, 25421200, 1305074809, 26015028256, 152759224512, 128024064000;
  1, 1296, 616326, 135459216, 14320729209, 694213330464, 13472453691584, 78340747014144, 65548320768000; ...

Seiichi Manyama, Rows n = 0..139, flattened

Cf. A000537, A000442, A008955, A107415, A130032.

{T(n,k)=polcoeff(prod(m=0,n,1 + m^3*x +x*O(x^n)),k)}
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))

cp's OEIS Frontend

A249677 Triangle, read by rows, with row n forming the coefficients in Product_{k=0..n} (1 + k^3*x).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI