A157057 Number of integer sequences of length n+1 with sum zero and sum of absolute values 16.
2, 48, 642, 6040, 44130, 264936, 1356194, 6077196, 24314490, 88206140, 293744154, 907129236, 2619716554, 7125357540, 18363363690, 45076309166, 105864434424, 238815143406, 519252051080, 1091481669390, 2224042468032, 4403475647758, 8489857618992, 15969368635950
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
Programs
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Mathematica
Table[(12870/16!)*n*(n+1)*(203212800 +349090560*n +487608192*n^2 +296058000*n^3 +196660016*n^4 +61391512*n^5 +25601072*n^6 +4564385*n^7 + 1344383*n^8 + 138621*n^9 +30835*n^10 +1715*n^11 +301*n^12 +7*n^13 +n^14), {n, 50}] (* G. C. Greubel, Jan 24 2022 *) -
Sage
[(12870/factorial(16))*n*(n+1)*(203212800 +349090560*n +487608192*n^2 +296058000*n^3 +196660016*n^4 +61391512*n^5 +25601072*n^6 +4564385*n^7 + 1344383*n^8 + 138621*n^9 +30835*n^10 +1715*n^11 +301*n^12 +7*n^13 +n^14) for n in (1..50)] # G. C. Greubel, Jan 24 2022
Formula
a(n) = T(n,8); 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 + 7*x + 49*x^2 + 147*x^3 + 441*x^4 + 735*x^5 + 1225*x^6 + 1225*x^7 + 1225*x^8 + 735*x^9 + 441*x^10 + 147*x^11 + 49*x^12 + 7*x^13 + x^14)/(1-x)^17. - Colin Barker, Jan 25 2013
a(n) = (12870/16!)*n*(n+1)*(203212800 + 349090560*n + 487608192*n^2 + 296058000*n^3 + 196660016*n^4 + 61391512*n^5 + 25601072*n^6 + 4564385*n^7 + 1344383*n^8 + 138621*n^9 + 30835*n^10 + 1715*n^11 + 301*n^12 + 7*n^13 + n^14). - G. C. Greubel, Jan 24 2022