A229360 Total sum of n-th powers of parts in all partitions of 9.

128, 270, 910, 4392, 26218, 177120, 1292410, 9924912, 78974938, 644749920, 5365004410, 45294444432, 386724933658, 3331246259520, 28899114836410, 252142576067952, 2210222303020378, 19448976596389920, 171690169932572410, 1519690359242075472, 13481625657159443098

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=9 of A213191.

Programs

Maple

a:= n-> 67+26*2^n+15*3^n+8*4^n+5*5^n+3*6^n+2*7^n+8^n+9^n:
seq(a(n), n=0..30);

Formula

a(n) = Sum_{k=1..9} A066633(9,k) * k^n.

a(n) = 67 + 26*2^n + 15*3^n + 8*4^n + 5*5^n + 3*6^n + 2*7^n + 8^n + 9^n.

G.f.: -2*(16152120*x^8 -31900986*x^7 [phone]*x^6 -11585520*x^5 +3083861*x^4 -505629*x^3 +50060*x^2 -2745*x +64) / Product_{j=1..9} (j*x-1).