A085438 a(n) = Sum_{i=1..n} binomial(i+1,2)^3.

1, 28, 244, 1244, 4619, 13880, 35832, 82488, 173613, 339988, 627484, 1102036, 1855607, 3013232, 4741232, 7256688, 10838265, 15838476, 22697476, 31958476, 44284867, 60479144, 81503720, 108503720, 142831845, 186075396, 240085548, 307008964, 389321839

Offset

1,2

References

Elisabeth Busser and Gilles Cohen, Neuro-Logies - "Chercher, jouer, trouver", La Recherche, April 1999, No. 319, page 97.

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = (90*n^7 +630*n^6 +1638*n^5 +1890*n^4+ 840*n^3 -48*n)/7!.

a(n) = (C(n+2, 3)/35)*(35 +210*C(n-1, 1) +399*C(n-1, 2) +315*C(n-1, 3) +90*C(n-1, 4)).

G.f.: x*(x^4+20*x^3+48*x^2+20*x+1) / (x-1)^8. - Colin Barker, May 02 2014

Example

a(10) = (90*(10^7)+630*(10^6)+1638*(10^5)+1890*(10^4)+840*(10^3)-48*(10))/5040 = 339988.

Mathematica

Table[(90*n^7 + 630*n^6 + 1638*n^5 + 1890*n^4 + 840*n^3 - 48*n)/7!, {n, 1, 50}] (* G. C. Greubel, Nov 22 2017 *)

Prog

(PARI) Vec(x*(x^4+20*x^3+48*x^2+20*x+1)/(x-1)^8 + O(x^100)) \\ Colin Barker, May 02 2014
(PARI) a(n) = sum(i=1, n, binomial(i+1, 2)^3); \\ Michel Marcus, Nov 22 2017
(Magma) [(90*n^7 +630*n^6 +1638*n^5 +1890*n^4+ 840*n^3 -48*n)/ Factorial(7): n in [1..30]]; // G. C. Greubel, Nov 22 2017

Crossrefs

Column k=3 of A334781.

Cf. A000292, A087127, A024166, A024166, A085439, A085440, A085441, A085442, A000332, A086020, A086021, A086022, A000389, A086023, A086024, A000579, A086025, A086026, A000580, A086027, A086028, A027555, A086029, A086030.

Sequence in context: A242436 A119544 A112797 * A188526 A219600 A092341

Adjacent sequences: A085435 A085436 A085437 * A085439 A085440 A085441

Keyword

easy,nonn

Author

André F. Labossière, Jun 30 2003

Extensions

More terms from Colin Barker, May 02 2014

Formula and example edited by Colin Barker, May 02 2014

Status

approved