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A157055 Number of integer sequences of length n+1 with sum zero and sum of absolute values 12. 1
2, 36, 362, 2570, 14240, 65226, 256508, 889716, 2777370, 7925720, 20934474, 51697802, 120353324, 265953170, 561075720, 1135620536, 2214405618, 4175000796, 7634582090, 13577591370, 23539760552, 39868752506, 66087441092, 107392877100, 171332460650, 268708978512 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
a(n) = T(n,6); 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 +5*x +25*x^2 +50*x^3 +100*x^4 +100*x^5 +100*x^6 +50*x^7 +25*x^8 +5*x^9 +x^10)/(1-x)^13. - Colin Barker, Jan 25 2013
From G. C. Greubel, Jan 24 2022: (Start)
a(n) = n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400.
E.g.f.: (x/518400)*(1036800 +8294400*x +22464000*x^2 +28728000*x^3 +20131200*x^4 +8369280*x^5 +2154240*x^6 +349200*x^7 +35400*x^8 +2160*x^9 +72*x^10 +x^11)*exp(x). (End)
MATHEMATICA
Table[n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400, {n, 50}] (* G. C. Greubel, Jan 24 2022 *)
PROG
(Sage) [n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400 for n in (1..50)] # G. C. Greubel, Jan 24 2022
CROSSREFS
Sequence in context: A126735 A229679 A119582 * A057407 A286266 A193127
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 22 2009
STATUS
approved

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Last modified June 23 13:32 EDT 2024. Contains 373648 sequences. (Running on oeis4.)