|
|
A027818
|
|
a(n) = (n+1)*binomial(n+6,6).
|
|
6
|
|
|
1, 14, 84, 336, 1050, 2772, 6468, 13728, 27027, 50050, 88088, 148512, 241332, 379848, 581400, 868224, 1268421, 1817046, 2557324, 3542000, 4834830, 6512220, 8665020, 11400480, 14844375, 19143306, 24467184, 31011904, 39002216, 48694800, 60381552, 74393088, 91102473
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Number of 13-subsequences of [ 1, n ] with just 6 contiguous pairs.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1+6*x)/(1-x)^8.
E.g.f.: (7! +9360*x +20520*x^2 +15000*x^3 +4650*x^4 +666*x^5 +43*x^6 + x^7)*exp(x)/7!. - G. C. Greubel, Aug 29 2019
Sum_{n>=0} 1/a(n) = Pi^2 - 5269/600.
Sum_{n>=0} (-1)^n/a(n) = Pi^2/2 - 512*log(2)/5 + 40189/600. (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(n+1)*Binomial[n+6, 6], {n, 0, 30}] (* G. C. Greubel, Aug 29 2019 *)
|
|
PROG
|
(Haskell)
a027818 n = (n + 1) * a007318' (n + 6) 6
(Magma) [(n+1)*Binomial(n+6, 6): n in [0..30]]; // G. C. Greubel, Aug 29 2019
(Sage) [(n+1)*binomial(n+6, 6) for n in (0..30)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..30], n-> (n+1)*Binomial(n+6, 6)); # G. C. Greubel, Aug 29 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|