A380886 - OEIS

%I #10 Feb 07 2025 09:11:52

%S 1,1,3,1,5,8,1,11,17,21,1,21,42,50,55,1,43,100,128,138,144,1,85,235,

%T 323,358,370,377,1,171,561,813,923,965,979,987,1,341,1331,2043,2378,

%U 2510,2559,2575,2584,1,683,3158,5150,6125,6527,6681,6737,6755,6765,1,1365,7503,12967,15772,16972,17441,17617,17680,17700,17711

%N Triangle T(n,k), 1<=k<=n: column k are the coefficients of the INVERT transform of Sum_{i=1..k} i*x^i.

%F T(n,k) = [x^n] 1/(1-x^1-2*x^2-3*x^3-4*x^4-...-k*x^k) .

%e The full array starts

%e   1    1    1    1    1    1    1    1    1    1

%e   1    3    3    3    3    3    3    3    3    3

%e   1    5    8    8    8    8    8    8    8    8

%e   1   11   17   21   21   21   21   21   21   21

%e   1   21   42   50   55   55   55   55   55   55

%e   1   43  100  128  138  144  144  144  144  144

%e   1   85  235  323  358  370  377  377  377  377

%e   1  171  561  813  923  965  979  987  987  987

%e   1  341 1331 2043 2378 2510 2559 2575 2584 2584

%e   1  683 3158 5150 6125 6527 6681 6737 6755 6765

%e but the non-interesting upper right triangular part is not put into the sequence.

%p A380886 := proc(n,k)

%p     local g,x ;

%p     g := 1/(1-add(i*x^i,i=1..k)) ;

%p     coeftayl(g,x=0,n) ;

%p end proc:

%p seq(seq( A380886(n,k),k=1..n),n=1..12) ;

%Y Cf. A001045 (column k=2), A101822 (column k=3), A322059 (column k=4?), A001906 (diagonal), A054452 (subdiagonal).

%K nonn,tabl,easy

%O 1,3

%A _R. J. Mathar_, Feb 07 2025