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 A098432 Coefficients of polynomials S(n,x) related to Springer numbers. 3
 1, 8, 7, 128, 304, 177, 3072, 13952, 21080, 10199, 98304, 724992, 2016000, 2441056, 1051745, 3932160, 42762240, 187643904, 407505664, 428605352, 169913511, 188743680, 2839019520, 17974591488, 60428242944, 111985428352 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..25. A. Randrianarivony and J. Zeng, Une famille des polynomes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26. FORMULA Recurrence: S(0, x)=1, S(n, x)=(2x+2)(2x+4)S(n-1, x+2)-(2x+1)^2S(n-1, x). G.f.: Sum[n>=0, S(n, x)t^n] = 1/(1+t-4*2(x+1)t/(1-4*2(x+2)t/(1+t-4*4(x+3)t/(1-4+4(x+4)t/...)))). EXAMPLE S(0,x) = 1, S(1,x) = 8*x + 7, S(2,x) = 128*x^2 + 304*x + 177, S(3,x) = 3072*x^3 + 13952*x^2 + 21080*x + 10199. PROG (PARI) S(n, x)=if(n<1, 1, (2*x+2)*(2*x+4)*S(n-1, x+2)-(2*x+1)^2*S(n-1, x)) CROSSREFS Cf. A001586. S(n, 1/2) = A000464(n+1), S(n, -1/2) = A000281(n). Leading coefficients are A051189. Constant terms are in A098433. Cf. A001586. S(n, 1/2) = A000464(n), S(n, -1/2) = A000281(n). Sequence in context: A038285 A354546 A261117 * A197623 A291692 A127583 Adjacent sequences: A098429 A098430 A098431 * A098433 A098434 A098435 KEYWORD tabl,nonn AUTHOR Ralf Stephan, Sep 07 2004 STATUS approved

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Last modified June 2 22:56 EDT 2023. Contains 363102 sequences. (Running on oeis4.)