A110327 Triangle read by rows: T(n,k) = n!*Pell(n-k+1)/k!, where Pell(n)=A000129(n).

1, 2, 1, 10, 4, 1, 72, 30, 6, 1, 696, 288, 60, 8, 1, 8400, 3480, 720, 100, 10, 1, 121680, 50400, 10440, 1440, 150, 12, 1, 2056320, 851760, 176400, 24360, 2520, 210, 14, 1, 39715200, 16450560, 3407040, 470400, 48720, 4032, 280, 16, 1, 862928640

Offset: 0

Author

Paul Barry, Jul 20 2005

Keywords

• nonn
• tabl
• easy

Comments

The row polynomials form an Appell sequence (see Wikipedia). - Tom Copeland, Dec 03 2013

Examples

			Rows begin:
  1;
  2,1;
  10,4,1;
  72,30,6,1;
  696,288,60,8,1;
  8400,3480,720,100,10,1;
  121680,50400,10440,1440,150,12,1;
		

Links

• Wikipedia, Appell sequence

Crossrefs

Cf. A000129, A110328 (row sums), A110329 (diagonal sums), A110330 (matrix inverse).

Formula

Column k has e.g.f.: x^k/(k!*(1-2*x-x^2)).

E.g.f.: Sum_{n>=0, k>=0} T(n,k)*x^n*y^k/n! = e^(x*y)/(1-2*x-x^2). - Franklin T. Adams-Watters, Jan 12 2007

Extensions

Edited by Franklin T. Adams-Watters, Jan 12 2007