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A064204 a(n) = 280*binomial(n+4,9) + 280*binomial(n+4,8) + 105*binomial(n+3,7) + 77*binomial(n+3,6) + 43*binomial(n+2,5) - 16*binomial(n+2,4) + 20*binomial(n+1,3) - floor(n*(n^2 - 1)*(n^2 - 4)*(n-3)/360). 1
0, 0, 4, 120, 1140, 6525, 27580, 94724, 279160, 730930, 1741300, 3839660, 7937644, 15535975, 29012620, 52014200, 89976240, 150801764, 245731940, 390446960, 606440100, 922712945, 1377845084, 2022497180, 2922412200, 4161985750, 5848482900, 8116985604 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

L. Berzolari, Allgemeine Theorie der Höheren Ebenen Algebraischen Kurven, Encyclopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Band III_2. Heft 3, Leipzig: B. G. Teubner, 1906. p. 353.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

L. Berzolari, Allgemeine Theorie der Höheren Ebenen Algebraischen Kurven, In: Meyer W.F., Mohrmann H. (eds) Geometrie. Vieweg+Teubner Verlag, Wiesbaden, 1921.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

G.f.: x^2*(4 + 80*x + 120*x^2 + 45*x^3 + 70*x^4 - 59*x^5 + 20*x^6) / (1 - x)^10. - Colin Barker, Feb 28 2012

From Colin Barker, Dec 21 2017: (Start)

a(n) = (n*(-720 + 1080*n + 404*n^2 - 1098*n^3 + 282*n^4 + 9*n^5 + 33*n^6 + 9*n^7 + n^8)) / 1296.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>9.

(End)

MATHEMATICA

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 0, 4, 120, 1140, 6525, 27580, 94724, 279160, 730930}, 40] (* Harvey P. Dale, Jul 29 2022 *)

PROG

(PARI) concat(vector(2), Vec(x^2*(4 + 80*x + 120*x^2 + 45*x^3 + 70*x^4 - 59*x^5 + 20*x^6) / (1 - x)^10 + O(x^40))) \\ Colin Barker, Dec 21 2017

CROSSREFS

Sequence in context: A283035 A284764 A271421 * A054644 A006434 A240397

Adjacent sequences:  A064201 A064202 A064203 * A064205 A064206 A064207

KEYWORD

nonn,easy

AUTHOR

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Sep 22 2001

STATUS

approved

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Last modified October 1 12:45 EDT 2022. Contains 357147 sequences. (Running on oeis4.)