A157053 Number of integer sequences of length n+1 with sum zero and sum of absolute values 8.
2, 24, 162, 780, 2970, 9492, 26474, 66222, 151560, 322190, 643632, 1219374, 2206932, 3838590, 6447660, 10501172, 16639974, 25727292, 38906870, 57671880, 83945862, 120177024, 169447302, 235597650, 323371100, 438575202, 588265524, 780951962, 1026829680
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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Mathematica
Table[n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576, {n,50}] (* G. C. Greubel, Jan 23 2022 *) -
Sage
[n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576 for n in (1..50)] # G. C. Greubel, Jan 23 2022
Formula
a(n) = T(n,4); 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+3*x+9*x^2+9*x^3+9*x^4+3*x^5+x^6)/(1-x)^9. - Colin Barker, Mar 17 2012
a(n) = n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576. - Bruno Berselli, Mar 17 2012
E.g.f.: (x/576)*(1152 +5760*x +9216*x^2 +6432*x^3 +2208*x^4 +384*x^5 +32*x^6 +x^7)*exp(x). - G. C. Greubel, Jan 23 2022