A179503 a(n) = Sum_{k=0..n} C(n,k)*sigma(n,k)*sigma(n,n-k) for n>0 with a(0)=1.

1, 2, 38, 352, 8372, 115584, 4900168, 109607936, 5462020742, 210689453568, 11579697409448, 585804318154752, 39828186864515408, 2482740302750253056, 188760627291893696552, 14430243196023615258624

Offset

0,2

Comments

sigma(n,k) denotes the sum of the k-th power of the divisors of n.

Links

Table of n, a(n) for n=0..15.

Example

a(2) = 1*2*5 + 2*3*3 + 1*5*2.
a(3) = 1*2*28 + 3*4*10 + 3*10*4 + 1*28*2.
a(4) = 1*3*273 + 4*7*73 + 6*21*21 + 4*73*7 + 1*273*3.
a(5) = 1*2*3126 + 5*6*626 + 10*26*126 + 10*126*26 + 5*626*6 + 1*3126*2.
a(6) = 1*4*47450 + 6*12*8052 + 15*50*1394 + 20*252*252 + 15*1394*50 + 6*8052*12 + 1*47450*4.

Prog

(PARI) a(n)=if(n==0, 1, sum(k=0, n, binomial(n, k)*sigma(n, k)*sigma(n, n-k)))

Crossrefs

Sequence in context: A226402 A217214 A303618 * A126731 A216357 A046845

Adjacent sequences: A179500 A179501 A179502 * A179504 A179505 A179506

Keyword

nonn

Author

Paul D. Hanna, Sep 21 2010

Status

approved