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 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. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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: A106151 A323467 A239959 * A215926 A007888 A188723 Adjacent sequences:  A214432 A214433 A214434 * A214436 A214437 A214438 KEYWORD sign,tabl AUTHOR Peter Luschny, Jul 17 2012 STATUS approved

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Last modified June 6 15:07 EDT 2020. Contains 334827 sequences. (Running on oeis4.)