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 A335311 Coefficients of polynomials arising in the series expansion of the multiplicative inverse of an analytic function. Irregular triangle read by rows. 0
 1, 1, 2, 2, 6, 12, 3, 24, 72, 24, 24, 4, 120, 480, 180, 360, 40, 120, 5, 720, 3600, 1440, 4320, 360, 2160, 720, 60, 240, 180, 6, 5040, 30240, 12600, 50400, 3360, 30240, 20160, 630, 5040, 3780, 7560, 84, 420, 840, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The coefficients of Bell-type polynomials where the monomials correspond to integer partitions. The monomials are in graded lexicographic order with variables x[0] > x[1] > ... > x[n]. This means that monomials are compared first by their total degree, with ties broken by lexicographic order. (This is the monomial order of Maple after sorting.) LINKS EXAMPLE The triangle starts (the refinement is indicated by square brackets): [0]    1; [1]    1; [2]    2,     2; [3]    6,    12,     3; [4]   24,    72,    (24,    24),    4; [5]  120,   480,   (180,   360),   (40,   120),     5; [6]  720,  3600,  (1440,  4320),  (360,  2160,   720), (60,  240,  180),    6; [7] 5040, 30240, (12600, 50400), (3360, 30240, 20160), (630, 5040, 3780, 7560), (84, 420, 840), 7; [8] 40320, 282240, (120960, 604800), (33600, 403200, 403200), (6720, 80640, 60480, 241920, 40320), (1008, 10080, 20160, 20160, 30240), (112, 672, 1680, 1120), 8; The multivariate polynomials start:         1         x[0]       2*x[0]^2 +          2*x[1]       6*x[0]^3 +    12*x[0]*x[1] +          3*x[2]      24*x[0]^4 +  72*x[0]^2*x[1] +    24*x[0]*x[2] +       24*x[1]^2 +       4*x[3]     120*x[0]^5 + 480*x[0]^3*x[1] + 180*x[0]^2*x[2] + 360*x[0]*x[1]^2 + 40*x[0]*x[3] + 120*x[1]*x[2] + 5*x[4] MAPLE A335311Triangle := proc(numrows) local ser, p, C, B, P; B(0) := 1; ser := series(1/B(s), s, numrows); C := [seq(expand(simplify(n!*coeff(ser, s, n))), n=0..numrows-1)]: P := subs(seq((D@@n)(B)(0)=n*x[n], n=1..numrows), C): for p in P do print(seq(abs(c), c=coeffs(sort(p)))) od end: A335311Triangle(8); CROSSREFS Cf. A199673 (row reversed refinement), A006153 (row sums),  A000041 (length of rows), A182779 (different monomial order). Sequence in context: A275312 A209026 A091764 * A192933 A079005 A281351 Adjacent sequences:  A335306 A335309 A335310 * A335312 A335313 A335314 KEYWORD nonn,tabf AUTHOR Peter Luschny, May 31 2020 STATUS approved

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Last modified August 5 05:22 EDT 2020. Contains 336209 sequences. (Running on oeis4.)