A157020 a(n) = Sum_{d|n} d*binomial(n/d+d-2,d-1).

1, 3, 4, 9, 6, 22, 8, 33, 28, 46, 12, 131, 14, 78, 136, 177, 18, 307, 20, 456, 302, 166, 24, 1149, 376, 222, 568, 1177, 30, 2387, 32, 1761, 958, 358, 2556, 5224, 38, 438, 1496, 7851, 42, 8317, 44, 4863, 9136, 622, 48, 20169, 6518, 11451, 3112, 8516, 54, 23734

Offset: 1

Author

R. J. Mathar, Feb 21 2009

Keywords

• easy
• nonn
• look

Comments

Equals row sums of triangle A157497. [Gary W. Adamson & Mats Granvik, Mar 01 2009]

Links

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

Crossrefs

Cf. A081543, A132065, A156833 (Mobius transform), A324158, A324159.

Programs

Maple

add( d*binomial(n/d+d-2,d-1),d=numtheory[divisors](n) ) ;

PARI

N=66; x='x+O('x^N); Vec(sum(k=1, N, k*x^k/(1-x^k)^k)) \\ Seiichi Manyama, Sep 03 2019

Formula

G.f.: Sum_{n>=1} n*x^n/(1-x^n)^n.