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A171273 Matrix inverse of the MacMahon numbers A060187 by way of recursive calculation. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A200486 A182496

Adjacent sequences:  A171270 A171271 A171272 * A171274 A171275 A171276

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula and Mats Granvik, Dec 06 2009

STATUS

approved

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Last modified April 22 10:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)