|
|
A101289
|
|
Inverse Moebius transform of 5-simplex numbers A000389.
|
|
9
|
|
|
1, 7, 22, 63, 127, 280, 463, 855, 1309, 2135, 3004, 4704, 6189, 9037, 11776, 16359, 20350, 27901, 33650, 44695, 53614, 68790, 80731, 103776, 118882, 148701, 171220, 210469, 237337, 292292, 324633, 393351, 438922, 522298, 576346, 690333, 749399
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{d|n} d*(d+1)*(d+2)*(d+3)*(d+4)/120. a(n) = Sum_{d|n} C(d+4,5). a(n) = Sum{d|n} A000389(d). a(n) = Sum_{d|n} (d^5-10*d^4+35*d^3-50*d^2+24*d)/120.
G.f.: Sum_{k>=1} x^k/(1 - x^k)^6 = Sum_{k>=1} binomial(k+4,5) * x^k/(1 - x^k). - Seiichi Manyama, Apr 19 2021
|
|
PROG
|
(PARI) a(n) = sumdiv(n, d, binomial(d+4, 5)); \\ Seiichi Manyama, Apr 19 2021
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+4, 5)*x^k/(1-x^k))) \\ Seiichi Manyama, Apr 19 2021
|
|
CROSSREFS
|
See also: A007437 = inverse Moebius transform of triangular numbers, A116963 = inverse Moebius transform of tetrahedral numbers. Cf. A073570.
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|