0,2

Row sums are A028859. Diagonal sums are A141015(n+1). Inverse is A154930. Product of A030528 and A007318.

Transforms sequence m^n with g.f. 1/(1-m*x) to the sequence with g.f. (1+x)/(1-(m+1)x-(m+1)x^2).

Riordan array ((1+x)/(1-x-x^2), x(1+x)/(1-x-x^2));

Triangle T(n,k)=sum{j=0..n, C(j+1,n-j)*C(j,k)}.

T(n,k)=T(n-1,k)+T(n-1,k-1)+T(n-2,k)+T(n-2,k-1), T(0,0)=1, T(1,0)=2, T(n,k)=0 if k>n . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 18 2009]

Sum_{k, 0<=k<=n}T(n,k)*x^k = A000045(n+1), A028859(n), A125145(n), A086347(n+1) for x=0,1,2,3 respectively. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 19 2009]

Triangle begins

1,

2, 1,

3, 4, 1,

5, 10, 6, 1,

8, 22, 21, 8, 1,

13, 45, 59, 36, 10, 1,

21, 88, 147, 124, 55, 12, 1,

34, 167, 339, 366, 225, 78, 14, 1,

55, 310, 741, 976, 770, 370, 105, 16, 1

Production array is

2, 1,

-1, 2, 1,

3, -1, 2, 1,

-10, 3, -1, 2, 1,

36, -10, 3, -1, 2, 1,

-137, 36, -10, 3, -1, 2, 1,

543, -137, 36, -10, 3, -1, 2, 1,

or ((1+x+sqrt(1+6x+5x^2))/2,x) beheaded.

T(5,3)=T(4,3)+T(4,2)+T(3,3)+T(3,2)=8+21+1+6=36 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 18 2009]

Sequence in context: A055888 A094442 A060642 this_sequence A049400 A106382 A004741

Adjacent sequences: A154926 A154927 A154928 this_sequence A154930 A154931 A154932

easy,nonn,tabl

Paul Barry (pbarry(AT)wit.ie), Jan 17 2009