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 A192924 Constant term in the reduction by (x^2->x+1) of the polynomial p(n,x) defined below at Comments. 2
 1, 0, 1, 4, 20, 115, 761, 5723, 48353, 454233, 4701724, 53204955, 653749199, 8670930456, 123500484305, 1880367585200, 30481594476514, 524197712831867, 9532792177527307, 182792169717039937, 3686148742978363201, 77989408383978583425 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The titular polynomial is defined by p(n,x)=n*p(n-1,x)+(x^2)*p(n-2,x), with p(0,x)=1, p(1,x)=x.  For discussions of polynomial reduction, see A192232, A192744, and A192872. LINKS FORMULA Conjecture: a(n) +2*(-n+1)*a(n-1) +(n^2-3*n-1)*a(n-2) +3*(n-2)*a(n-3) +a(n-4)=0. - R. J. Mathar, May 08 2014 MATHEMATICA q = x^2; s = x + 1; z = 22; p[0, x_] := 1; p[1, x_] := x; p[n_, x_] := n*p[n - 1, x] + p[n - 2, x]*x^2; Table[Expand[p[n, x]], {n, 0, 7}] reduce[{p1_, q_, s_, x_}] := FixedPoint[(s PolynomialQuotient @@ #1 +        PolynomialRemainder @@ #1 &)[{#1, q, x}] &, p1] t = Table[reduce[{p[n, x], q, s, x}], {n, 0, z}]; u1 = Table[Coefficient[Part[t, n], x, 0], {n, 1, z}]   (* A192924 *) u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]   (* A192925 *) CROSSREFS Cf. A192232, A192744, A192925. Sequence in context: A171802 A100034 A341919 * A258664 A231539 A106567 Adjacent sequences:  A192921 A192922 A192923 * A192925 A192926 A192927 KEYWORD nonn AUTHOR Clark Kimberling, Jul 12 2011 STATUS approved

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Last modified June 26 16:52 EDT 2022. Contains 354885 sequences. (Running on oeis4.)