0,5

This means the description of A038200 is slightly incorrect and ought be: "Row sums of triangle K(m,n), inverse to a triangle obtained from A020921 after eliminating the leftmost column."

G.f.: (1/(1+x))*Sum(x^(k-1)/((1+x)^k-y*x^k),k=1..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 26 2008

If the leftmost column of the triangle in A020921 is deleted we get

1

1 1

2 3 1

2 5 4 1

4 10 10 5 1

2 11 19 15 6 1

6 21 35 35 21 7 1

4 22 52 69 56 28 8 1

6 33 83 126 126 84 36 9 1

The present triangle is the inverse of this, namely

1

-1 1

1 -3 1

-1 7 -4 1

1 -15 10 -5 1

-1 31 -19 15 -6 1

1 -63 28 -35 21 -7 1

-1 127 -28 71 -56 28 -8 1

with row sums 1,0,-1,3,-8,21,-54,134,-318,720 of A038200.

A020921 := proc(n, k) option remember; local divs; if n <= 0 then 1; elif k > n then 0; else divs := numtheory[divisors](n); add(numtheory[mobius](op(i, divs))*binomial(n/op(i, divs), k), i=1..nops(divs)); fi; end: A020921t := proc(n, k) option remember; A020921(n+1, k+1); end: TriLInv := proc(nmax) local a, row, col; a := array(0..nmax, 0..nmax); for row from 0 to nmax do for col from row+1 to nmax do a[row, col] := 0; od; od; for row from 0 to nmax do for col from row to 0 by -1 do if row <> col then a[row, col] := -add(a[row, c]*A020921t(c, col), c=col+1..row)/A020921t(col, col); else a[row, col] := (1-add(a[row, c]*A020921t(c, col), c=col+1..row))/A020921t(col, col); fi; od; od; RETURN(a); end: nmax := 12 : a := TriLInv(nmax) : for row from 0 to nmax do for col from 0 to row do printf("%d, ", a[row, col]); od; od:

Cf. A039912.

Sequence in context: A116407 A135288 A078026 this_sequence A140068 A121300 A128119

Adjacent sequences: A126710 A126711 A126712 this_sequence A126714 A126715 A126716

sign,tabl

R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 12 2007