0,3

The e.g.f. of the m-th (unsigned) column sequence without leading zeros of the generalized (a=2) Laguerre triangle L(2; n+m,m)= A062139(n+m,m), n >= 0, is N(2; m,x)/(1-x)^(3+2*m), with the row polynomials N(2; m,x) := sum(a(m,k)*x^k,k=0..m).

Comments from Zerinvary Lajos (zlaja(AT)freemail.hu), Apr 01 2005: Formatted as a square array:

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

C(5,3)*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(8,5)

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

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

C(9,7)*C(7,0), C(10,7)*C(8,1)

C(10,8)*C(8,0)

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

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

A062145, A062190.

Sequence in context: A021318 A068437 A016477 this_sequence A103247 A030523 A123965

Adjacent sequences: A062193 A062194 A062195 this_sequence A062197 A062198 A062199

nonn,tabl

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