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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 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-François Alcover, Aug 09 2018, from PARI *) PROG (PARI) T(n, k)=if(n

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