A157058 Number of integer sequences of length n+1 with sum zero and sum of absolute values 18.

2, 54, 812, 8580, 70310, 472626, 2703512, 13507416, 60110030, 241925530, 891454124, 3037849828, 9654482474, 28818500830, 81289041680, 217815522736, 556959705302, 1364497268946, 3214138597460, 7302195414780, 16045139112002, 34183012888134, 70764981877592

Offset: 1

Author

R. H. Hardin, Feb 22 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A103881, A156554.

Programs

Mathematica

Table[(48620/18!)*n*(n+1)*(14631321600 [phone]*n [phone]*n^2 [phone]*n^3 [phone]*n^4 [phone]*n^5 [phone]*n^6 [phone]*n^7 [phone]*n^8 [phone]*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 *)

Sage

[(48620/factorial(18))*n*(n+1)*(14631321600 [phone]*n [phone]*n^2 [phone]*n^3 [phone]*n^4 [phone]*n^5 [phone]*n^6 [phone]*n^7 [phone]*n^8 [phone]*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

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 [phone]*n [phone]*n^2 [phone]*n^3 [phone]*n^4 [phone]*n^5 [phone]*n^6 [phone]*n^7 [phone]*n^8 [phone]*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