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A157056 Number of integer sequences of length n+1 with sum zero and sum of absolute values 14. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A202865 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

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Last modified October 7 08:31 EDT 2022. Contains 357270 sequences. (Running on oeis4.)