A046900 Triangle inverse to that in A046899.

1, -1, 1, 1, -3, 2, 1, 3, -10, 6, -1, 9, 10, -42, 24, -17, 21, 50, 42, -216, 120, -107, -33, 230, 294, 216, -1320, 720, -415, -1173, 670, 1974, 1944, 1320, -9360, 5040, 1231, -13515, -4510, 11130, 17064, 14520, 9360, -75600, 40320, 56671, -113739, -131230, 20202, 136296, 157080, 121680, 75600

Offset

0,5

Comments

Sequence gives numerators; denominators are A001813.

References

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

Links

Table of n, a(n) for n=0..52.

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

Example

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

Maple

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

Mathematica

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-François Alcover, Aug 08 2012, after Emeric Deutsch *)

Crossrefs

Cf. A001813, A046899.

Sequence in context: A331523 A025261 A111572 * A365367 A270828 A325315

Adjacent sequences: A046897 A046898 A046899 * A046901 A046902 A046903

Keyword

sign,tabl,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Jun 25 2005

Status

approved