0,3

Comment from Zerinvary Lajos (zlaja(AT)freemail.hu), Mar 24 2005: Formatted as an upper right triangle:

C(0,0)*C(3,0),C(1,1)*C(4,0),C(2,2)*C(5,0),C(3,3)*C(6,0), C(4,4)*C(7,0),C(5,5)*C(8,0),C(6,6)*C(9,0),C(7,7)*C(10,0),C(8,8*C(11,0)

C(1,0)*C(4,1),C(2,1)*C(5,1),C(3,2)*C(6,1),C(4,3)*C(7,1), C(5,4)*C(8,1), C(6,5)*C(9,1),C(7,6)*C(10,1),C(8,7)*C(11,1)

C(2,0)*C(5,2),C(3,1)*C(6,2),C(4,2)*C(7,2),C(5,3)*C(8,2), C(6,4)*C(9,2),C(7,2)*C(10,2),C(8,6)*C(11,2)

C(3,0)*C(6,3),C(4,1)*C(7,3),C(5,2)*C(8,3),C(6,3)* C(9,3), C(7,4)*C(10,3),C(8,3)*C(11,3)

C(4,0)*C(7,4),C(5,1)*C(8,4),C(6,2)*C(9,4),C(7,3)*C(10,4), C(8,4)*C(11,4)

C(5,0)*C(8,5),C(6,1)*C(9,5),C(7,2)*C(10,5),C(8,3)*C(11,5)

C(6,0)*C(9,6),C(7,1)*C(10,6),C(8,2)*C(11,6)

C(7,0)*C(10,7),C(8,1)*C(11,7)

C(8,0)*C(11,8)

The e.g.f. of the m-th (unsigned) column sequence without leading zeros of the generalized (a=3) Laguerre triangle L(3; n+m, m)= A062137(n+m, m), n >= 0, is N(3; m, x)/(1-x)^(2*(m+2)), with the row polynomials N(3; m, x) := sum(a(m, k)*x^k, k=0..m).

N(3; m, x) := ((1-x)^(2*(m+2)))*diff((x^m)/(m!*(1-x)^(m+4)), x$m); a(m, k)= [x^k]N(3; m, x).

N(3; m, x)= sum((binomial(m, j)*(2*m+3-j)!/((m+3)!*(m-j)!))*(x^(m-j))*(1-x)^j, j=0..m).

As a square array (from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2006):

1 1 1 1 1 1 1 1 1 ...

4 10 18 28 40 54 70 88 ...

10 45 126 280 540 945 1540 ...

20 140 560 1680 4200 9240 ...

35 350 1890 7350 23100 ...

56 756 5292 25872 ...

...

Cf. A000292.

Sequence in context: A039806 A030320 A104713 this_sequence A019213 A019128 A121463

Adjacent sequences: A062142 A062143 A062144 this_sequence A062146 A062147 A062148

nonn,tabl

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 19 2001