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A086022 a(n) = Sum_{i=1..n} C(i+2,3)^4. 19
1, 257, 10257, 170257, 1670882, 11505378, 61292514, 268652514, 1009853139, 3352413139, 10042998755, 27598188771, 70457539396, 168802499396, 382616259396, 825980472132, 1707628231653, 3396588391653, 6525595601653, 12150082161653, 21987344308134, 38769279231910 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: x*(1+x)*(x^8 +242*x^7 +6508*x^6 +43174*x^5 +84950*x^4 +43174*x^3 +6508*x^2 +242*x + 1) / (x-1)^14 . - R. J. Mathar, Dec 22 2013

(n-1)^4*a(n) +(-2*n^4 -4*n^3 -30*n^2 -28*n -17)*a(n-1) +(n+2)^4*a(n-2)=0. - R. J. Mathar, Dec 22 2013

a(n) = C(n+3,4)*[-41*F3(n) +350*(47*C(n+8,9) + 1749*C(n+7,9) + 9292*C(n+6,9) + 9292*C(n+5,9) + 1749*C(n+4,9) + 47*C(n+3,9))]/15015, where F3(n) = -C(3,0)*C(n+3,0) + C(4,1)*C(n+3,1) - C(5,2)*C(n+3,2) + C(6,3)*C(n+3,3). The value of F3(n), (n=0..8) is: 1, 35, 119, 273, 517, 871, 1355, 1989, 2793, ... - Yahia Kahloune, Dec 23 2013

a(n) = (n/12972960)*(-8856 + 60060*n^2 + 165165*n^3 + 841841*n^4 + 2462460*n^5 + 3709420*n^6 + 3243240*n^7 + 1756755*n^8 + 600600*n^9 + 126490*n^10 + 15015*n^11 + 770*n^12). - G. C. Greubel, Nov 22 2017

EXAMPLE

a(8) = C(11,4)*[-41*2793 + 350*(47*C(16,9) + 1749*C(15,9) + 9292*C(14,9) + 9292*C(13,9) + 1749*C(12,9) + 47*C(11,9))]/15015 = 268652514 .

MATHEMATICA

Accumulate[Binomial[Range[3, 30], 3]^4] (* Harvey P. Dale, Oct 09 2016 *)

PROG

(PARI) for(n=1, 30, print1((n/12972960)*(-8856 + 60060*n^2 + 165165*n^3 + 841841*n^4 + 2462460*n^5 + 3709420*n^6 + 3243240*n^7 + 1756755*n^8 + 600600*n^9 + 126490*n^10 + 15015*n^11 + 770*n^12), ", ")) \\ G. C. Greubel, Nov 22 2017

(MAGMA) [(n/12972960)*(-8856 +60060*n^2 +165165*n^3 +841841*n^4 +2462460*n^5 +3709420*n^6 +3243240*n^7 +1756755*n^8 +600600*n^9 +126490*n^10 +15015*n^11 +770*n^12): n in [1..30]]; // G. C. Greubel, Nov 22 2017

CROSSREFS

Cf. A086020, A086021, A086023, A086024, A086025, A086026, A086027, A086028, A086029, A086030, A087127, A024166, A085438, A085439, A085440, A085441, A085442.

Sequence in context: A301552 A279641 A168116 * A125649 A219549 A219548

Adjacent sequences:  A086019 A086020 A086021 * A086023 A086024 A086025

KEYWORD

easy,nonn

AUTHOR

André F. Labossière, Jul 11 2003

STATUS

approved

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Last modified October 16 03:28 EDT 2019. Contains 328040 sequences. (Running on oeis4.)