|
|
A056115
|
|
a(n) = n*(n+11)/2.
|
|
18
|
|
|
0, 6, 13, 21, 30, 40, 51, 63, 76, 90, 105, 121, 138, 156, 175, 195, 216, 238, 261, 285, 310, 336, 363, 391, 420, 450, 481, 513, 546, 580, 615, 651, 688, 726, 765, 805, 846, 888, 931, 975, 1020, 1066, 1113, 1161, 1210, 1260, 1311, 1363, 1416, 1470, 1525
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
REFERENCES
|
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(6-5*x)/(1-x)^3.
If we define f(n,i,a) = Sum_{k=0..n-i} ( binomial(n,k)*stirling1(n-k,i) *Product_{j=0..k-1} (-a-j) ), then a(n) = -f(n,n-1,6), for n>=1. - Milan Janjic, Dec 20 2008
Sum_{n>=1} 1/a(n) = 83711/152460. - R. J. Mathar, Jul 14 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/11 - 20417/152460. - Amiram Eldar, Jan 10 2021
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) [n*(n+11)/2: n in [0..50]]; // G. C. Greubel, Jan 18 2020
(Sage) [n*(n+11)/2 for n in (0..50)] # G. C. Greubel, Jan 18 2020
(GAP) List([0..50], n-> n*(n+11)/2 ); # G. C. Greubel, Jan 18 2020
|
|
CROSSREFS
|
Third column of Pascal (1, 6) triangle A096956.
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|