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A046900 Triangle inverse to that in A046899. 1

%I

%S 1,-1,1,1,-3,2,1,3,-10,6,-1,9,10,-42,24,-17,21,50,42,-216,120,-107,

%T -33,230,294,216,-1320,720,-415,-1173,670,1974,1944,1320,-9360,5040,

%U 1231,-13515,-4510,11130,17064,14520,9360,-75600,40320,56671,-113739,-131230,20202,136296,157080,121680,75600

%N Triangle inverse to that in A046899.

%C Sequence gives numerators; denominators are A001813.

%D H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83.

%H H. W. Gould, <a href="/A007680/a007680.pdf">A class of binomial sums and a series transform</a>, Utilitas Math., 45 (1994), 71-83. (Annotated scanned copy)

%e 1; -1/2 1/2; 1/12 -3/12 2/12; ...

%p with(linalg): b:=proc(n,k) if k<=n then binomial(n+k,k) else 0 fi end: bb:=(n,k)->b(n-1,k-1): B:=matrix(12,12,bb): A:=inverse(B): a:=(n,k)->((2*n-2)!/(n-1)!)*A[n,k]: for n from 0 to 10 do seq(a(n,k),k=1..n) od; # yields sequence in triangular form - _Emeric Deutsch_

%t max = 10; b[n_, k_] := If[k <= n, Binomial[n+k, k], 0]; BB = Table[b[n, k], {n, 0, max-1}, {k, 0, max-1}]; AA = Inverse[BB]; a[n_, k_] := ((2n-2)!/(n-1)!)*AA[[n, k]]; Flatten[ Table[ a[n, k], {n, 1, max}, {k, 1, n}]] (* _Jean-Fran├žois Alcover_, Aug 08 2012, after _Emeric Deutsch_ *)

%Y Cf. A046899.

%K sign,tabl,easy,nice

%O 0,5

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Jun 25 2005

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)