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%I #17 Feb 13 2024 07:54:13
%S 1,1,5,1,12,15,1,21,63,35,1,32,168,224,70,1,45,360,840,630,126,1,60,
%T 675,2400,3150,1512,210,1,77,1155,5775,11550,9702,3234,330,1,96,1848,
%U 12320,34650,44352,25872,6336,495
%N Coefficient triangle of certain polynomials N(4; m,x).
%C 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.
%F 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))).
%F 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).
%Y Family of polynomials (see A062145): A008459 (c=1), A132813 (c=2), A062196 (c=3), A062145 (c=4), this sequence (c=5), A062190 (c=6).
%K nonn,tabl
%O 0,3
%A _Wolfdieter Lang_, Jun 19 2001
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