A229358 Total sum of n-th powers of parts in all partitions of 7.

54, 105, 311, 1281, 6407, 35745, 212951, 1323441, 8464487, 55247745, 365983991, 2451448401, 16559916167, 112602093345, 769628452631, 5282089330161, 36372360161447, 251135368228545, 1737811434946871, 12047233511096721, 83642479068080327, 581449745964789345

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=7 of A213191.

Programs

Maple

a:= n-> 30+11*2^n+6*3^n+3*4^n+2*5^n+6^n+7^n:
seq(a(n), n=0..30);

Formula

a(n) = Sum_{k=1..7} A066633(7,k) * k^n.

a(n) = 30 + 11*2^n + 6*3^n + 3*4^n + 2*5^n + 6^n + 7^n.

G.f.: -(196356*x^6 -339112*x^5 +230407*x^4 -79457*x^3 +14759*x^2 -1407*x +54) / Product_{j=1..7} (j*x-1).