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A104986 Matrix logarithm of triangle A104980. 4
0, 1, 0, 2, 2, 0, 7, 4, 3, 0, 33, 14, 7, 4, 0, 191, 66, 27, 11, 5, 0, 1297, 382, 137, 48, 16, 6, 0, 10063, 2594, 843, 270, 79, 22, 7, 0, 87669, 20126, 6041, 1820, 495, 122, 29, 8, 0, 847015, 175338, 49219, 14176, 3679, 848, 179, 37, 9, 0, 8989301, 1694030, 448681, 124828, 31361, 6930, 1371, 252, 46, 10, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Column 0 equals column 1 of triangular matrix A104980, which satisfies: SHIFT_LEFT(column 0 of A104980^p) = p*(column p+1 of A104980) for p>=0. Column 1 equals twice column 0.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n, 0) = A104981(n), T(n+1, 1) = 2*T(n, 0) for n>=0.

EXAMPLE

Triangle begins:

0;

1,0;

2,2,0;

7,4,3,0;

33,14,7,4,0;

191,66,27,11,5,0;

1297,382,137,48,16,6,0;

10063,2594,843,270,79,22,7,0;

87669,20126,6041,1820,495,122,29,8,0;

847015,175338,49219,14176,3679,848,179,37,9,0;

8989301,1694030,448681,124828,31361,6930,1371,252,46,10,0; ...

MATHEMATICA

nmax = 10;

M = Table[If[n == k, 0, If[n == k+1, -n+1, -Coefficient[(1-1/Sum[i! x^i, {i, 0, n}])/x + O[x]^n, x, n-k-1]]], {n, 1, nmax+1}, {k, 1, nmax+1}];

T[n_, k_] /; 0 <= k <= n := Sum[(-1)^p MatrixPower[M, p][[n+1, k+1]]/p, {p, 1, n+1}]; T[_, _] = 0;

Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Aug 09 2018, from PARI *)

PROG

(PARI) T(n, k)=if(n<k || k<0, 0, sum(p=1, n+1, (-1)^p*(matrix(n+1, n+1, m, j, if(m==j, 0, if(m==j+1, -m+1, -polcoeff((1-1/sum(i=0, m, i!*x^i))/x+O(x^m), m-j-1))))^p)[n+1, k+1]/p))

CROSSREFS

Cf. A104980, A104981 (column 0), A104987 (row sums).

Sequence in context: A323675 A243492 A086118 * A060007 A021457 A305605

Adjacent sequences:  A104983 A104984 A104985 * A104987 A104988 A104989

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Apr 10 2005

STATUS

approved

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Last modified October 25 19:28 EDT 2020. Contains 338012 sequences. (Running on oeis4.)