0,3

The e.g.f. of the m-th (unsigned) column sequence without leading zeros of the generalized (a=5) Laguerre triangle L(5; n+m,m)= A062138(n+m,m), n >= 0, is N(5; m,x)/(1-x)^(2*(m+3)), with the row polynomials N(5; 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(0,0)*C(5,0), C(1,1)*C(6,0), C(2,2)*C(7,0), C(3,3)*C(8,0), C(4,4)*C(9,0), C(5,5)*C(10,0), C(6,6)*C(11,0), C(7,7)*C(12,0), C(8,8)*C(13,0)

C(1,0)*C(6,1), C(2,1)*C(7,1), C(3,2)*C(8,1), C(4,3)*C(9,1), C(5,4)*C(10,1), C(6,5)*C(11,1), C(7,6)*C(12,1), C(8,7)*C(13,1)

C(2,0)*C(7,2), C(3,1)*C(8,2), C(4,2)*C(9,2), C(5,3)*C(10,2), C(6,4)*C(11,2), C(7,5)*C(12,2), C(8,6)*C(13,2)

C(3,0)*C(8,3), C(4,1)*C(9,3), C(5,2)*C(10,3), C(6,3)*C(11,3), C(7,4)*C(12,3), C(8,5)*C(13,3)

C(4,0)*C(9,4), C(5,1)*C(10,4), C(6,2)*C(11,4), C(7,3)*C(12,4), C(8,4)*C(13,4)

C(5,0)*C(10,5), C(6,1)*C(11,5), C(7,2)*C(12,5), C(8,3)*C(13,5)

C(6,0)*C(11,6), C(7,1)*C(12,6), C(8,2)*C(13,6)

C(7,0)*C(12,7), C(8,1)*C(13,7)

C(8,0)*C(13,8)

a(m, k)= [x^k]N(5; m, x), with N(5; m, x)= ((1-x)^(2*(m+3)))*diff((x^m)/(m!*(1-x)^(m+6)), x$m).

N(5; m, x)= sum((binomial(m, j)*(2*m+5-j)!/((m+5)!*(m-j)!))*(x^(m-j))*(1-x)^j, j=0..m).

A062145.

Sequence in context: A163945 A013613 A122508 this_sequence A080211 A146997 A147483

Adjacent sequences: A062187 A062188 A062189 this_sequence A062191 A062192 A062193

nonn,tabl

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