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Triangle T(n,k) = [x^k] n!*(n+1+x^n)*Sum_{i=0..n-1} x^i/(i+1).
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%I #6 Feb 03 2019 06:47:46

%S 2,1,6,3,2,1,24,12,8,6,3,2,120,60,40,30,24,12,8,6,720,360,240,180,144,

%T 120,60,40,30,24,5040,2520,1680,1260,1008,840,720,360,240,180,144,120,

%U 40320,20160,13440,10080,8064,6720,5760,5040,2520,1680,1260,1008,840,720,362880

%N Triangle T(n,k) = [x^k] n!*(n+1+x^n)*Sum_{i=0..n-1} x^i/(i+1).

%C The coefficient in front of x^k of the polynomial n!*(n+1+x^n)*Sum_{i=0..n-1} x^i/(i+1), columns k=0..2n-1.

%F Row sums: (n+2)*A000254(n).

%e The triangle starts

%e 2, 1;

%e 6, 3, 2, 1;

%e 24, 12, 8, 6, 3, 2;

%e 120, 60, 40, 30, 24, 12, 8, 6;

%p P := proc(n,k) (n+1+x^n)*add( x^i/(i+1),i=0..n-1) ; coeftayl(expand(%),x=0,k) ; end:

%p T := proc(n,k) n!*P(n,k) ; end:

%p for n from 1 to 10 do for k from 0 to 2*n-1 do printf("%d,",T(n,k)) ; od: od: # _R. J. Mathar_, Apr 09 2009

%Y Cf. A130679 (table Q), A158442.

%K nonn,easy,tabf

%O 1,1

%A _Paul Curtz_, Mar 19 2009

%E Edited by _R. J. Mathar_, Apr 09 2009