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A062196 Coefficient triangle of certain polynomials N(2; m,x). 16
1, 1, 3, 1, 8, 6, 1, 15, 30, 10, 1, 24, 90, 80, 15, 1, 35, 210, 350, 175, 21, 1, 48, 420, 1120, 1050, 336, 28, 1, 63, 756, 2940, 4410, 2646, 588, 36, 1, 80, 1260, 6720, 14700, 14112, 5880, 960, 45, 1, 99, 1980, 13860, 41580, 58212, 38808, 11880, 1485, 55 (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=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_{k=0..m} a(m,k)*x^k.

From Zerinvary Lajos, Apr 01 2005: (Start)

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). (End)

LINKS

Table of n, a(n) for n=0..54.

FORMULA

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

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

a(n,m) = C(n,m)*(C(n+1,m)+C(n+1,m-1)). - Vladimir Kruchinin, Apr 06 2018

CROSSREFS

Cf. A062145, A062190.

Sequence in context: A258205 A258018 A188939 * A103247 A030523 A207815

Adjacent sequences:  A062193 A062194 A062195 * A062197 A062198 A062199

KEYWORD

nonn,tabl

AUTHOR

Wolfdieter Lang, Jun 19 2001

STATUS

approved

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Last modified October 13 18:14 EDT 2019. Contains 327981 sequences. (Running on oeis4.)