|
|
A274501
|
|
a(n) = 25*binomial(n-1,6) + binomial(n-1,5).
|
|
3
|
|
|
0, 1, 31, 196, 756, 2226, 5502, 12012, 23892, 44187, 77077, 128128, 204568, 315588, 472668, 689928, 984504, 1376949, 1891659, 2557324, 3407404, 4480630, 5821530, 7480980, 9516780, 11994255, 14986881, 18576936, 22856176, 27926536, 33900856, 40903632, 49071792
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
5,3
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x^6*(1 + 24*x)/(1-x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
a(n) = (n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(25*n-144)/720. - Wesley Ivan Hurt, Jun 25 2016
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[25 Binomial[n - 1, 6] + Binomial[n - 1, 5], {n, 5, 40}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 31, 196, 756, 2226, 5502}, 40] (* Harvey P. Dale, Mar 09 2022 *)
|
|
PROG
|
(Magma) [25*Binomial(n-1, 6)+Binomial(n-1, 5): n in [5..40]];
(PARI) concat(0, Vec(x^6*(1+24*x)/(1-x)^7 + O(x^99))) \\ Altug Alkan, Jun 27 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|