A171273 Matrix inverse of the MacMahon numbers A060187 by way of recursive calculation.

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

Offset

1,4

Comments

Row sums are:

{1, 2, 12, 232, 15024, 3190176, 2150247104, 4495724480128, 28750797892487936,

557764883306639383040, 32668026499694843494640640,...}

Links

Table of n, a(n) for n=1..34.

Formula

m=2;

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

Example

{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}

Mathematica

Clear[t, M, a, m] 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[%]

Crossrefs

A060187, A055325, A154921,

Sequence in context: A216808 A293107 A113106 * A157832 A330660 A200486

Adjacent sequences: A171270 A171271 A171272 * A171274 A171275 A171276

Keyword

nonn,uned

Author

Roger L. Bagula and Mats Granvik, Dec 06 2009

Status

approved