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

1,1

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A103881, A156554.

Sequence in context: A241623 A288443 A108476 * A279853 A052411 A073066

Adjacent sequences: A157050 A157051 A157052 * A157054 A157055 A157056

Keyword

nonn,easy

Author

R. H. Hardin, Feb 22 2009

Status

approved