A229357 Total sum of n-th powers of parts in all partitions of 6.

35, 66, 180, 660, 2904, 14196, 73920, 400620, 2229624, 12637956, 72573360, 420738780, 2456635944, 14422057716, 85023813600, 502907704140, 2982460443864, 17724476245476, 105513644666640, 628987635392700, 3753738850485384, 22422625749793236, 134041199563164480

Offset: 0

Author

Alois P. Heinz, Sep 20 2013

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Row n=6 of A213191.

Programs

Maple

a:= n-> 19+8*2^n+4*3^n+2*4^n+5^n+6^n:
seq(a(n), n=0..30);

Formula

a(n) = Sum_{k=1..6} A066633(6,k) * k^n.

a(n) = 19 + 8*2^n + 4*3^n + 2*4^n + 5^n + 6^n.

G.f.: -(18144*x^5 -28874*x^4 +17295*x^3 -4919*x^2 +669*x -35) / Product_{j=1..6} (j*x-1).