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A171274 Matrix inverse of A142458. 1
1, -1, 1, 7, -8, 1, -235, 273, -39, 1, 35353, -41116, 5928, -166, 1, -22683409, 26382125, -3804940, 106900, -677, 1, 60147266239, -69954818244, 10089231945, -283474190, 1796973, -2724, 1, -648088191536203, 753764796604717, -108711714513099, 3054442698125 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums of the absolute values are 1, 2, 16, 548, 82564, 52978052, 140476590316, 1513638537322988, 65723264907190519444, 11454000890648520042077732, 7996985842928165507025527197516, ...

LINKS

Table of n, a(n) for n=1..32.

FORMULA

Sum_{j=k..n} T(n,j)*A142458(j,k) = delta(n,k).

EXAMPLE

The triangle starts as:

1;

-1, 1;

7, -8, 1;

-235, 273, -39, 1;

35353, -41116, 5928, -166, 1;

-22683409, 26382125, -3804940, 106900, -677, 1;

60147266239, -69954818244, 10089231945, -283474190, 1796973, -2724, 1;

MAPLE

A142458 := proc(n, k) if n = k then 1; elif k > n or k < 1 then 0 ; else (3*n-3*k+1)*procname(n-1, k-1)+(3*k-2)*procname(n-1, k) ; end if; end proc:

A171274 := proc(n, k) option remember; if k > n or k < 1 then 0 ; elif k= n then 1/A142458(n, n) ; else -add( procname(n, j)*A142458(j, k), j=k+1..n) ; %/A142458(k, k) ; end if; end proc:

seq(seq(A171274(n, k), k=1..n), n=1..10) ; # R. J. Mathar, Jun 04 2011

MATHEMATICA

Clear[t, M, a, m] m = 3; 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[%] (* note the sign toggling of the input in M[] which generates absolute values, |T(., .)| *)

CROSSREFS

Cf. A142458.

Sequence in context: A154216 A258947 A216207 * A126625 A154169 A245260

Adjacent sequences:  A171271 A171272 A171273 * A171275 A171276 A171277

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula and Mats Granvik, Dec 06 2009

STATUS

approved

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Last modified April 21 22:12 EDT 2019. Contains 322328 sequences. (Running on oeis4.)