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A062264 Coefficient triangle of certain polynomials N(4; m,x). 4
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 (list; table; graph; refs; listen; history; text; internal format)
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.

From Zerinvary Lajos, Apr 01 2005: (Start)

Formatted as a square array:

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

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

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

C(3,3)*C(7,3), C(4,3)*C(8,3), C(5,3)*C(9,3), C(6,3)*C(10,3), C(7,3)*C(11,3), C(8,3)*C(12,3)

C(4,4)*C(8,4), C(5,4)*C(9,4), C(6,4)*C(10,4), C(7,4)*C(11,4), C(8,4)*C(12,4)

C(5,5)*C(9,5), C(6,5)*C(10,5), C(7,5)*C(11,5), C(8,5)*C(12,5)

C(6,6)*C(10,6), C(7,6)*C(11,6), C(8,6)*C(12,6)

C(7,7)*C(11,7), C(8,7)*C(12,7)

C(8,8)*C(12,8). (End)

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

Cf. A062196, A062145, A062190.

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

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Last modified March 29 18:31 EDT 2020. Contains 333117 sequences. (Running on oeis4.)