A157056 Number of integer sequences of length n+1 with sum zero and sum of absolute values 14.

2, 42, 492, 4060, 26070, 137886, 623576, 2476296, 8809110, 28512110, 85014204, 235895244, 614266354, 1511679210, 3536846160, 7907476016, 16967926746, 35078339106, 70098276620, 135798494460, 255689552382, 468969729382, 839584669992, 1469778991800, 2520031983950

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 (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Formula

a(n) = T(n,7); 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 +6*x +36*x^2 +90*x^3 +225*x^4 +300*x^5 +400*x^6 +300*x^7 +225*x^8 +90*x^9 +36*x^10 +6*x^11 +x^12)/(1-x)^15. - Colin Barker, Jan 25 2013

From G. C. Greubel, Jan 24 2022: (Start)

a(n) = n*(n+1)*(n^12 +6*n^11 +197*n^10 +930*n^9 +12363*n^8 +43938*n^7 +300551*n^6 +751710*n^5 +2756536*n^4 +4309656*n^3 +7816752*n^2 +5780160*n +3628800)/25401600.

E.g.f.: (x/25401600)*(50803200 +482630400*x +1574899200*x^2 +2472422400*x^3 +2176070400*x^4 +1169320320*x^5 +403683840*x^6 +92221920*x^7 +14129640*x^8 +1449420*x^9 +97608*x^10 +4116*x^11 +98*x^12 +x^13)*exp(x). (End)

Mathematica

Table[n*(n+1)*(n^12 +6*n^11 +197*n^10 +930*n^9 +12363*n^8 +43938*n^7 +300551*n^6 +751710*n^5 +2756536*n^4 +4309656*n^3 +7816752*n^2 +5780160*n +3628800)/25401600, {n, 50}] (* G. C. Greubel, Jan 24 2022 *)

Prog

(Sage) [n*(n+1)*(n^12 +6*n^11 +197*n^10 +930*n^9 +12363*n^8 +43938*n^7 +300551*n^6 +751710*n^5 +2756536*n^4 +4309656*n^3 +7816752*n^2 +5780160*n +3628800)/25401600 for n in (1..50)] # G. C. Greubel, Jan 24 2022

Crossrefs

Cf. A103881, A156554.

Sequence in context: A360786 A070808 A229474 * A180425 A140170 A318247

Adjacent sequences: A157053 A157054 A157055 * A157057 A157058 A157059

Keyword

nonn,easy

Author

R. H. Hardin, Feb 22 2009

Status

approved