A214435 Triangle read by rows: T(n,k) = n!*S(n,k), where S(n,k) is the matrix inverse of the triangle zeta(k-n,1) - zeta(k-n,k+1), n>=1, k>=1.

1, -1, 1, 1, -3, 2, 3, 3, -12, 6, -2, 30, 8, -60, 24, -240, 240, 240, 0, -360, 120, -3900, -540, 4800, 1800, -360, -2520, 720, -15120, -112560, 65520, 70560, 12600, -5880, -20160, 5040, 2169888, -4284000, -756672, 2076480, 945504, 70560, -80640, -181440, 40320

Offset

1,5

References

J. Faulhaber, Academia Algebrae, Darinnen die miraculosische inventiones zu den höchsten Cossen weiters continuirt und profitirt werden, Augspurg, bey Johann Ulrich Schönigs, 1631.

Links

Table of n, a(n) for n=1..45.

Example

                     1,
                   -1, 1,
                  1, -3, 2,
                3, 3, -12, 6,
             -2, 30, 8, -60, 24,
        -240, 240, 240, 0, -360, 120,
-3900, -540, 4800, 1800, -360, -2520, 720.

Maple

with(linalg): S := proc(n) f := (n, k) -> `if`(k>n, 0, Zeta(0, k-n, 1)-Zeta(0, k-n, k+1)); inverse(matrix(n, n, f)) end: A214435_row := n -> n!*convert(row(S(n), n), list); for n from 1 to 9 do A214435_row(n) od;

Mathematica

max = 9; s = Table[ If[ k > n, 0, Zeta[k - n, 1] - Zeta[k - n, k + 1]], {n, 1, max}, {k, 1, max}] // Inverse; t[n_, k_] := n!*s[[n, k]]; Table[t[n, k], {n, 1, max}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 02 2013 *)

Crossrefs

Cf. A103438.

Sequence in context: A323467 A341097 A239959 * A215926 A007888 A188723

Adjacent sequences: A214432 A214433 A214434 * A214436 A214437 A214438

Keyword

sign,tabl

Author

Peter Luschny, Jul 17 2012

Status

approved