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A101289 Inverse Moebius transform of 5-simplex numbers A000389. 7
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

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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.

Cf. A000389, A007437, A116963, A332508.

Sequence in context: A308579 A246831 A122238 * A085287 A278767 A286186

Adjacent sequences:  A101286 A101287 A101288 * A101290 A101291 A101292

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Mar 31 2006

STATUS

approved

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Last modified August 3 21:09 EDT 2021. Contains 346441 sequences. (Running on oeis4.)