OFFSET
1,2
REFERENCES
A. Umar, B. Yushau and B. M. Ghandi, (2006), "Patterns in convolution of two series", in Stewart, S. M., Olearski, J. E. and Thompson, D. (Eds), Proceedings of the Second Annual Conference for Middle East Teachers of Science, Mathematics and Computing (pp. 95-101). METSMaC: Abu Dhabi.
A. Umar, B. Yushau and B. M. Ghandi, "Convolution of two series", Australian Senior Maths. Journal, 21(2) (2007), 6-11.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
C. P. Neuman and D. I. Schonbach, Evaluation of sums of convolved powers using Bernoulli numbers, SIAM Rev. 19 (1977), no. 1, 90--99. MR0428678 (55 #1698). See Table 2. - N. J. A. Sloane, Mar 23 2014
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
a(n) = C(n+2, 3)*(n^8 + 8*n^7 + 29*n^6 + 62*n^5 + 86*n^4 + 80*n^3 + 28*n^2 - 24*n + 192)/462.
G.f.: x*(x^4 + 26*x^3 + 66*x^2 + 26*x + 1)^2/(x-1)^12. [Colin Barker, Jul 08 2012]
EXAMPLE
a(3) = 1510 because 1(3^5)+(2^5)(2^5)+(3^5)1= 1510
MAPLE
f:=n->(n^11-22*n^5+231*n^3-210*n)/2772;
[seq(f(n), n=0..50)]; # N. J. A. Sloane, Mar 23 2014
MATHEMATICA
CoefficientList[Series[(x^4 + 26 x^3 + 66 x^2 + 26 x + 1)^2/(x - 1)^12, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *)
PROG
(Magma) [Binomial(n+2, 3)*(n^8+8*n^7+29*n^6+62*n^5+86*n^4 +80*n^3+28*n^2-24*n+192)/462: n in [1..40]]; // Vincenzo Librandi, Mar 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Abdullahi Umar, Oct 05 2008
STATUS
approved