A085439 a(n) = Sum_{i=1..n} binomial(i+1,2)^4.

1, 82, 1378, 11378, 62003, 256484, 871140, 2550756, 6651381, 15802006, 34776742, 71791798, 140366759, 261917384, 469277384, 811379400, 1359360681, 2214396762, 3517606762, 5462416762, 8309813083, 12406965164, 18209748140, 26309748140, 37466388765, 52644875166

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 13.

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

Formula

a(n) = (2520*n^9 +22680*n^8 +79920*n^7 +136080*n^6 +107352*n^5 +22680*n^4 -10080*n^3 +1728*n)/9!.

G.f.: x*(x^6+72*x^5+603*x^4+1168*x^3+603*x^2+72*x+1) / (x-1)^10. - Colin Barker, May 02 2014

Example

a(15) = (2520*(15^9) +22680*(15^8) +79920*(15^7) +136080*(15^6) +107352*(15^5) +22680*(15^4) -10080*(15^3) +1728*15)/9! = 469277384.

Mathematica

Table[(2520*(n^9) + 22680*(n^8) + 79920*(n^7) + 136080*(n^6) + 107352*(n^5) + 22680*(n^4) - 10080*(n^3) + 1728*n)/9!, {n, 1, 50}] (* G. C. Greubel, Nov 22 2017 *)

Prog

(PARI) Vec(x*(x^6+72*x^5+603*x^4+1168*x^3+603*x^2+72*x+1)/(x-1)^10 + O(x^100)) \\ Colin Barker, May 02 2014
(PARI) a(n) = sum(i=1, n, binomial(i+1, 2)^4); \\ Michel Marcus, Nov 22 2017
(Magma) [(2520*n^9 +22680*n^8 +79920*n^7 +136080*n^6 +107352*n^5 +22680*n^4 -10080*n^3 +1728*n)/Factorial(9): n in [1..30]]; // G. C. Greubel, Nov 22 2017

Crossrefs

Column k=4 of A334781.

Cf. A000292, A087127, A024166, A024166, A085438, A085440, A085441, A085442, A000332, A086020, A086021, A086022, A000389, A086023, A086024, A000579, A086025, A086026, A000580, A086027, A086028, A027555, A086029, A086030.

Sequence in context: A263812 A160154 A093282 * A282155 A280857 A281603

Adjacent sequences: A085436 A085437 A085438 * A085440 A085441 A085442

Keyword

easy,nonn

Author

André F. Labossière, Jul 03 2003

Extensions

More terms from Colin Barker, May 02 2014

Typo in example fixed by Colin Barker, May 02 2014

Status

approved