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 A154852 Triangle of coefficients of p(x,n) = (1/4)*(1-x)^(n+1)*Sum_{m >= 0} ((2*m- 1)^n - (2*m+3)^n)*x^m, read by rows. 4
 0, -1, 1, -2, 0, 2, -7, -3, 3, 7, -20, -56, 0, 56, 20, -61, -415, -370, 370, 415, 61, -182, -2632, -5710, 0, 5710, 2632, 182, -547, -15155, -64407, -49735, 49735, 64407, 15155, 547, -1640, -82896, -619696, -1085840, 0, 1085840, 619696, 82896, 1640 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums are zero. LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA Rows are coefficients of p(x,n) = (1/4)*(1-x)^(n+1)*Sum_{m >= 0} ((2*m-1)^n - (2*m+3)^n)*x^m. EXAMPLE Triangle begins as:       0;      -1,      1;      -2,      0,       2;      -7,     -3,       3,        7;     -20,    -56,       0,       56,    20;     -61,   -415,    -370,      370,   415,      61;    -182,  -2632,   -5710,        0,  5710,    2632,    182;    -547, -15155,  -64407,   -49735, 49735,   64407,  15155,   547;   -1640, -82896, -619696, -1085840,     0, 1085840, 619696, 82896, 1640; MATHEMATICA T[n_, k_, p_, q_, r_, t_]:= SeriesCoefficient[(1/p)*(1-x)^(n+1)*Sum[((q*j+r)^n - (q*j+t)^n)*x^j, {j, 0, n}], {x, 0, k}]; Table[T[n, k, 4, 2, -1, 3], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Mar 11 2021 *) PROG (Sage) def f(n, p, q, r, t, x) : return (1/p)*(1-x)^(n+1)*sum( ((q*j+r)^n - (q*j+t)^n )*x^j for j in (0..n)) [[( f(n, 4, 2, -1, 3, x) ).series(x, n+1).list()[k] for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 11 2021 CROSSREFS Cf. A154853, A154854, A154855. Sequence in context: A185343 A161014 A235712 * A088996 A211888 A293783 Adjacent sequences:  A154849 A154850 A154851 * A154853 A154854 A154855 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Jan 16 2009 EXTENSIONS Edited by G. C. Greubel, Mar 11 2021 STATUS approved

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Last modified April 23 10:57 EDT 2021. Contains 343204 sequences. (Running on oeis4.)