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 A111926 Expansion of x^4/((1-2*x)*(x^2-x+1)*(x-1)^2). 1
 0, 0, 0, 0, 1, 5, 15, 36, 78, 162, 331, 671, 1353, 2718, 5448, 10908, 21829, 43673, 87363, 174744, 349506, 699030, 1398079, 2796179, 5592381, 11184786, 22369596, 44739216, 89478457, 178956941, 357913911, 715827852, 1431655734, 2863311498 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Binomial transform of sequence (0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0). Note: the binomial transform of the sequence (0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0) is A111927; the binomial transform of the sequence (0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0) is A024495 (disregarding first two terms, which are both zero). LINKS Index entries for linear recurrences with constant coefficients, signature (5,-10,11,-7,2). FORMULA a(n+2) - a(n+1) + a(n) = A000295(n) = 2^n - n - 1 (Eulerian numbers); a(n) = 1/3*2^n-n+2/3*(1/2+1/2*I*sqrt(3))^n*(-1/4-1/4*I*sqrt(3))+2/3*(1/2-1/2*I*sqrt(3))^n*(-1/4+1/4*I*sqrt(3)) a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(n)=5*a(n-1)-10*a(n-2)+ 11*a(n-3)- 7*a(n-4)+2*a(n-5). - Harvey P. Dale, Feb 24 2016 MATHEMATICA CoefficientList[Series[x^4/((1-2x)(x^2-x+1)(x-1)^2), {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -10, 11, -7, 2}, {0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, Feb 24 2016 *) PROG Floretion Algebra Multiplication Program, FAMP Code: -4ibaseisumseq[ + .5'i + .5'j + .5'k + .5'ij' + .5'jk' + .5'ki' + e], sumtype: Y[8] = (int)Y[6] - (int)Y[7] + Y[8] + sum (internal program code). CROSSREFS Cf. A000295, A111927, A024495. Sequence in context: A144898 A163250 A053808 * A137609 A109818 A146797 Adjacent sequences:  A111923 A111924 A111925 * A111927 A111928 A111929 KEYWORD easy,nonn AUTHOR Creighton Dement, Aug 21 2005 STATUS approved

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