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 A097182 G.f. A(x) has the property that the first (n+1) terms of A(x)^(n+1) form the n-th row polynomial R_n(y) of triangle A097181 and satisfy R_n(1/2) = 8^n for all n>=0. 4
 1, 7, 21, 21, -63, -231, -15, 1521, 3073, -4319, -29631, -29631, 143361, 489345, -255, -3342591, -6684671, 9454081, 64553985, 64553985, -311689215, -1064175615, -4095, 7266627585, 14533263361, -20553129983, -140345589759, -140345589759, 677648531457, 2313636773889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA G.f.: A(x) = 16*x/(1-(1-2*x)^8). EXAMPLE A(x) = 1 + 7*x + 21*x^2 + 21*x^3 - 63*x^4 - 231*x^5 - 15*x^6 +-... For n>=0, the first (n+1) coefficients of A(x)^(n+1) forms the n-th row polynomial R_n(y) of triangle A097181: A^1={1,_7,21,21,-63,-231,-15,1521,3073,...} A^2={1,14,_91,336,609,-462,-5469,-9516,...} A^3={1,21,210,_1288,5103,11655,2160,-85590,...} A^4={1,28,378,3220,_18907,77280,199860,153000,...} A^5={1,35,595,6475,49910,_283192,1175190,3282870,...} A^6={1,42,861,11396,108402,778596,_4296034,17959968,...} These row polynomials satisfy: R_n(1/2) = 8^n: 8^1 = 1 + 14/2; 8^2 = 1 + 21/2 + 210/2^2; 8^3 = 1 + 28/2 + 378/2^2 + 3220/2^3; 8^4 = 1 + 35/2 + 595/2^2 + 6475/2^3 + 49910/2^4. PROG (PARI) a(n)=polcoeff(16*x/(1-(1-2*x)^8+x*O(x^n), n, x) CROSSREFS Cf. A097181, A097183, A097184, A097185. Sequence in context: A158280 A201072 A200935 * A058525 A219036 A063469 Adjacent sequences:  A097179 A097180 A097181 * A097183 A097184 A097185 KEYWORD sign AUTHOR Paul D. Hanna, Aug 03 2004 STATUS approved

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Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)