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

1,1

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A103881, A156554.

Sequence in context: A231654 A005429 A035606 * A290690 A013523 A260846

Adjacent sequences: A157054 A157055 A157056 * A157058 A157059 A157060

Keyword

nonn,easy

Author

R. H. Hardin, Feb 22 2009

Status

approved