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A111670 Array T(n,k) read by antidiagonals: the k-th column contains the first column of the k-th power of A039755. 1
1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 4, 15, 24, 1, 1, 5, 28, 105, 116, 1, 1, 6, 45, 280, 929, 648, 1, 1, 7, 66, 585, 3600, 9851, 4088, 1, 1, 8, 91, 1056, 9865, 56240, 121071, 28640, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

First few columns of the array generated from A039775 are: 1, 1, 1, 1, 1, 1, ...; 1, 2, 6, 24, 116, 648, ...; 1, 3, 15, 105, 929, ...; 1, 4, 28, 280, 3600, ...; 1, 5, 45, 585, 9865, ...;

LINKS

Table of n, a(n) for n=1..45.

FORMULA

Let A039755 (an analog of Stirling numbers of the second kind) be an infinite lower triangular matrix M; then the vector M^k * [1, 0, 0, 0, ...] (first column of the k-th power) is the k-th column of this array.

EXAMPLE

1 1 1 1 1 1 1 1

1 2 3 4 5 6 7 8

1 6 15 28 45 66 91 120

1 24 105 280 585 1056 1729 2640

1 116 929 3600 9865 22036 43001 76224

1 648 9851 56240 203565 565096 1318023 2717856

1 4088 121071 1029920 4953205 17148936 47920803 115146816

1 28640 1685585 21569600 138529105 600001696 2012844225 5644055040

MAPLE

A111670 := proc(n, k)

local A, i, j ;

A := Matrix(n, n) ;

for i from 1 to n do

for j from 1 to n do

A[i, j] := A039755(i-1, j-1) ;

end do:

end do:

LinearAlgebra[MatrixPower](A, k) ;

%[n, 1] ;

end proc:

for d from 2 to 12 do

for n from 1 to d-1 do

printf("%d, ", A111670(n, d-n)) ;

end do:

end do: # R. J. Mathar, Jan 27 2023

CROSSREFS

Cf. A039755, A007405 (column 2), A000384 (row 2), A011199 (row 3).

Sequence in context: A287024 A107702 A174480 * A123353 A156540 A156582

Adjacent sequences: A111667 A111668 A111669 * A111671 A111672 A111673

KEYWORD

nonn,tabl,changed

AUTHOR

Gary W. Adamson, Aug 14 2005

EXTENSIONS

Definition simplified by R. J. Mathar, Jan 27 2023

STATUS

approved

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Last modified January 30 02:40 EST 2023. Contains 359939 sequences. (Running on oeis4.)