login
A306721
a(n) = Sum_{k=0..n} binomial(k, 7*(n-k)).
2
1, 1, 1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1717, 3433, 6437, 11456, 19569, 32505, 53449, 89149, 155041, 286825, 564929, 1163317, 2442210, 5117225, 10558381, 21308121, 41973391, 80778601, 152344397, 282855561, 520060249, 953217792, 1753553441, 3256528177, 6127896977, 11694334137
OFFSET
0,9
FORMULA
G.f.: (1-x)^6/((1-x)^7-x^8).
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-8) for n > 7.
a(n) = A017857(7*n).
MATHEMATICA
a[n_] := Sum[Binomial[k, 7*(n-k)], {k, 0, n}]; Array[a, 40, 0] (* Amiram Eldar, Jun 21 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(k, 7*(n-k)))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7-x^8))
CROSSREFS
Column 7 of A306680.
Cf. A017857.
Sequence in context: A328268 A330346 A280351 * A306852 A275425 A373912
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 06 2019
STATUS
approved