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A062145 Coefficient triangle of certain polynomials N(3; m,x). 19
1, 1, 4, 1, 10, 10, 1, 18, 45, 20, 1, 28, 126, 140, 35, 1, 40, 280, 560, 350, 56, 1, 54, 540, 1680, 1890, 756, 84, 1, 70, 945, 4200, 7350, 5292, 1470, 120, 1, 88, 1540, 9240, 23100, 25872, 12936, 2640, 165, 1, 108 (list; table; graph; refs; listen; history; internal format)
OFFSET

0,3

COMMENTS

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)

FORMULA

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).

EXAMPLE

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 ...

...

CROSSREFS

Cf. A000292.

Sequence in context: A186368 A185676 A182971 * A178216 A019213 A019128

Adjacent sequences:  A062142 A062143 A062144 * A062146 A062147 A062148

KEYWORD

nonn,tabl

AUTHOR

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

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Last modified February 16 17:11 EST 2012. Contains 205938 sequences.