OFFSET
0,2
COMMENTS
Convolution of triangular numbers (A000217) and enneagonal numbers (A001106). - Bruno Berselli, Jul 21 2015
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = C(n+4, 4)*(7*n+5)/5.
G.f.: (1+6*x)/(1-x)^6.
From Wesley Ivan Hurt, May 02 2015: (Start)
a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6).
a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120. (End)
E.g.f.: (5! +1320*x +2040*x^2 +920*x^3 +145*x^4 +7*x^5)*exp(x)/5!
MAPLE
MATHEMATICA
Table[(n+1)(n+2)(n+3)(n+4)(7n+5)/120, {n, 0, 40}] (* Vincenzo Librandi, May 03 2015 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 12, 57, 182, 462, 1008}, 40] (* Harvey P. Dale, May 05 2022 *)
PROG
(Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120 : n in [0..40]]; // Wesley Ivan Hurt, May 02 2015
(PARI) vector(40, n, (7*n-2)*binomial(n+3, 4)/5) \\ G. C. Greubel, Aug 29 2019
(Sage) [(7*n+5)*binomial(n+4, 4)/5 for n in (0..40)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..40], n-> (7*n+5)*Binomial(n+4, 4)/5); # G. C. Greubel, Aug 29 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, Dec 14 1999
STATUS
approved