A120493 Triangle T(n,k) read by rows ; multiply row n of Pascal's triangle (A007318) by A024175(n).

1, 1, 1, 2, 4, 2, 5, 15, 15, 5, 14, 56, 84, 56, 14, 42, 210, 420, 420, 210, 42, 132, 792, 1980, 2640, 1980, 792, 132, 428, 2996, 8988, 14980, 14980, 8988, 2996, 428, 1416, 11328, 39648, 79296, 99120, 79296, 39648, 11328, 1416

Offset

0,4

Comments

Triangle given by [1, 1, 1, 1, 1, 1, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

Links

Table of n, a(n) for n=0..44.

Formula

T(n,k)=A007318(n,k)*A024175(n).

T(n,k)=6*T(n-1,k)+6*T(n-1,k-1)-10*T(n-2,k)-20*T(n-2,k-1)-10*T(n-2,k-2)+4*T(n-3,k)+12*T(n-3,k-1)+12*T(n-3,k-2)+4*T(n-3,k-3) for n>3, T(0,0)=T(1,0)=T(1,1)=1, T(2,0)=T(2,2)=2, T(2,1)=4, T(3,0)=T(3,3)=5, T(3,1)=T(3,2)=15, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Nov 22 2013

G.f.: (-1 +5*x +5*x*y -6*x^2 -12*x^2*y -6*x^2*y^2 +x^3 +3*x^3*y +3*x^3*y^2 +x^3*y^3)/( (-1+2*x+2*x*y) *(2*x^2*y^2+4*x^2*y+2*x^2-4*x*y-4*x+1) ). - R. J. Mathar, Aug 12 2015

Example

Triangle begins:
1;
1, 1;
2, 4, 2;
5, 15, 15, 5;
14, 56, 84, 56, 14;
42, 210, 420, 420, 210, 42;
132, 792, 1980, 2640, 1980, 792, 132;
428, 2996, 8988, 14980, 14980, 8988, 2996, 428;
1416, 11328, 39648, 79296, 99120, 79296, 39648, 11328, 1416 ;...

Crossrefs

Sequence in context: A117903 A167685 A268740 * A085880 A055883 A366588

Adjacent sequences: A120490 A120491 A120492 * A120494 A120495 A120496

Keyword

nonn,tabl

Author

Philippe Deléham, Aug 05 2006

Status

approved