A171273 Matrix inverse of A060187.

1, 1, 1, 5, 6, 1, 93, 115, 23, 1, 5993, 7436, 1518, 76, 1, 1272089, 1578757, 322762, 16330, 237, 1, 857402029, 1064110290, 217560951, 11012540, 160571, 722, 1, 1792650585525, 2224835452407, 454875884137, 23025275075, 335768223, 1512581, 2179, 1

Offset: 1

Author

Roger L. Bagula and Mats Granvik, Dec 06 2009

Keywords

• nonn
• uned
• tabl

Examples

			{1},
{1, 1},
{5, 6, 1},
{93, 115, 23, 1},
{5993, 7436, 1518, 76, 1},
{1272089, 1578757, 322762, 16330, 237, 1},
{857402029, 1064110290, 217560951, 11012540, 160571, 722, 1},
{1792650585525, 2224835452407, 454875884137, 23025275075, 335768223, 1512581, 2179, 1},
{11464255554367057, 14228139328931096, 2908996087466828, 147249943814184, 2147290464886, 9673492136, 13945196, 6552, 1},
{222406320165016449457, 276025608122908733321, 56434463826320585284, 2856645864675796564, 41657391444153086, 187665608020478, 270538484020, 127141156, 19673, 1},
{13026233415367869864109781, 16166689855580307839632286, 3305339964838291288943901, 167312402773377971746920, 2439853795947184617546, 10991486289326969076, 15845312257310658, 7446608913000, 1152338433, 59038, 1}
		

Crossrefs

Cf. A060187, A055325, A154921,

Programs

Mathematica

m = 2;
A[n_, 1] := 1
A[n_, n_] := 1
A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]
a = Table[A[n, k], {n, 12}, {k, n}]
M[n_] := Table[If[k <= m, (-1)^(m + k)*a[[m, k]], 0], {k, 1, n}, {m, 1, n}]
Table[Table[Inverse[M[12]][[m, n]], {m, 1, n}], {n, 1, 11}]
Flatten[%]

Formula

A(n,k) = (m*n - m*k + 1) * A(n - 1, k - 1) + (m*k - (m - 1)) * A(n - 1, k), A(n,1) = A(n,n) = 1.