A062264 Coefficient triangle of certain polynomials N(4; m,x).

1, 1, 5, 1, 12, 15, 1, 21, 63, 35, 1, 32, 168, 224, 70, 1, 45, 360, 840, 630, 126, 1, 60, 675, 2400, 3150, 1512, 210, 1, 77, 1155, 5775, 11550, 9702, 3234, 330, 1, 96, 1848, 12320, 34650, 44352, 25872, 6336, 495

Offset

0,3

Comments

The e.g.f. of the m-th (unsigned) column sequence without leading zeros of the generalized (a=4) Laguerre triangle L(4; n+m,m) = A062140(n+m,m), n >= 0, is N(4; m,x)/(1-x)^(5+2*m), with the row polynomials N(4; m,x) := Sum_{k=0..m} a(m,k)*x^k.

Links

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

Formula

a(m, k) = [x^k]N(4; m, x), with N(4; m, x) = ((1-x)^(5+2*m))*(d^m/dx^m)((x^m)/(m!*(1-x)^(m+5))).

N(4; m, x) = Sum_{j=0..m} (binomial(m, j)*(2*m+4-j)!/((m+4)!*(m-j)!)*(x^(m-j))*(1-x)^j).

Crossrefs

Family of polynomials (see A062145): A008459 (c=1), A132813 (c=2), A062196 (c=3), A062145 (c=4), this sequence (c=5), A062190 (c=6).

Sequence in context: A125232 A116923 A327797 * A276738 A094049 A286254

Adjacent sequences: A062261 A062262 A062263 * A062265 A062266 A062267

Keyword

nonn,tabl

Author

Wolfdieter Lang, Jun 19 2001

Status

approved