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 A194938 Triangle read by rows: coefficients of polynomials p(x,n) defined by 1/(1-t-t^2)^x=Sum_{n=1..oo} p(x,n)*t^n/n!. 1
 1, 0, 1, 0, 3, 1, 0, 8, 9, 1, 0, 42, 59, 18, 1, 0, 264, 450, 215, 30, 1, 0, 2160, 4114, 2475, 565, 45, 1, 0, 20880, 43512, 30814, 9345, 1225, 63, 1, 0, 236880, 528492, 420756, 154609, 27720, 2338, 84, 1, 0, 3064320, 7235568, 6316316, 2673972, 594489, 69552 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A039692 is a similar triangle but without the leading column. 1/(1-t-t^2) is the g.f. for the Fibonacci numbers (A000045). Row sums: A005442(n-1). REFERENCES Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150 LINKS EXAMPLE Triangle begins 1; 0, 1; 0, 3, 1; 0, 8, 9, 1; 0, 42, 59, 18, 1; 0, 264, 450, 215, 30, 1; 0, 2160, 4114, 2475, 565, 45, 1; 0, 20880, 43512, 30814, 9345, 1225, 63, 1; 0, 236880, 528492, 420756, 154609, 27720, 2338, 84, 1; 0, 3064320, 7235568, 6316316, 2673972, 594489, 69552, 4074, 108, 1; 0, 44634240, 110499696, 103889700, 49087520, 12803175, 1887753, 154350, 6630, 135, 1; MATHEMATICA p[t_] = 1/(1 - t - t^2)^x; Table[ ExpandAll[n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Cf. A000045, A005442, A039692 Sequence in context: A052420 A162971 A078521 * A135871 A126178 A094753 Adjacent sequences:  A194935 A194936 A194937 * A194939 A194940 A194941 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Apr 17 2008 EXTENSIONS Edited by N. J. A. Sloane, Aug 28 2011 STATUS approved

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