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 A157058 Number of integer sequences of length n+1 with sum zero and sum of absolute values 18. 1
 2, 54, 812, 8580, 70310, 472626, 2703512, 13507416, 60110030, 241925530, 891454124, 3037849828, 9654482474, 28818500830, 81289041680, 217815522736, 556959705302, 1364497268946, 3214138597460, 7302195414780, 16045139112002, 34183012888134, 70764981877592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (19,-171,969,-3876,11628,-27132,50388,-75582, 92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1). FORMULA a(n) = T(n,9); T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k). G.f.: 2*x*(1 +8*x +64*x^2 +224*x^3 +784*x^4 +1568*x^5 +3136*x^6 +3920*x^7 +4900*x^8 +3920*x^9 +3136*x^10 +1568*x^11 +784*x^12 +224*x^13 +64*x^14 +8*x^15 +x^16)/(1-x)^19. - Colin Barker, Jan 25 2013 a(n) = (48620/18!)*n*(n+1)*(14631321600 +26760222720*n +38452817664*n^2 +25217041536*n^3 +17311651344*n^4 +5993468992*n^5 +2592460808*n^6 +533444296*n^7 +163476113*n^8 +20735776*n^9 +4812092*n^10 +370160*n^11 +67942*n^12 +2912*n^13 +436*n^14 +8*n^15 +n^16). - G. C. Greubel, Jan 24 2022 MATHEMATICA Table[(48620/18!)*n*(n+1)*(14631321600 +26760222720*n +38452817664*n^2 +25217041536*n^3 +17311651344*n^4 +5993468992*n^5 +2592460808*n^6 +533444296*n^7 +163476113*n^8 +20735776*n^9 +4812092*n^10 +370160*n^11 +67942*n^12 +2912*n^13 +436*n^14 +8*n^15 +n^16), {n, 50}] (* G. C. Greubel, Jan 24 2022 *) PROG (Sage) [(48620/factorial(18))*n*(n+1)*(14631321600 +26760222720*n +38452817664*n^2 +25217041536*n^3 +17311651344*n^4 +5993468992*n^5 +2592460808*n^6 +533444296*n^7 +163476113*n^8 +20735776*n^9 +4812092*n^10 +370160*n^11 +67942*n^12 +2912*n^13 +436*n^14 +8*n^15 +n^16) for n in (1..50)] # G. C. Greubel, Jan 24 2022 CROSSREFS Cf. A103881, A156554. Sequence in context: A202739 A055024 A057411 * A305693 A357421 A071798 Adjacent sequences: A157055 A157056 A157057 * A157059 A157060 A157061 KEYWORD nonn,easy AUTHOR R. H. Hardin, Feb 22 2009 STATUS approved

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Last modified August 4 04:10 EDT 2024. Contains 374905 sequences. (Running on oeis4.)