A226065 Sum of all the smaller parts raised to their corresponding larger parts of the partitions of n into exactly two parts.

0, 1, 1, 5, 9, 44, 114, 564, 1882, 9665, 39083, 211025, 993803, 5686104, 30342060, 184813048, 1095555260, 7118824417, 46199135453, 320295658577, 2250749112381, 16626717667348, 125452246988974, 985178854556524

Offset: 1

Author

Wesley Ivan Hurt, May 24 2013

Keywords

• nonn
• easy

Examples

			a(6) = 44; 6 has exactly 3 partitions into two parts: (5,1),(4,2),(3,3). Raising the smaller parts to their corresponding larger parts and adding the results, we get: 1^5 + 2^4 + 3^3 = 1 + 16 + 27 = 44.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500
• Index entries for sequences related to partitions

Crossrefs

Cf. A226140.

Programs

Mathematica

Table[Sum[i^(n - i), {i, Floor[n/2]}], {n,50}] (* G. C. Greubel, Dec 13 2016 *)

PARI

a(n)=sum(i=1,floor(n/2),i^(n-i)) \\ Ralf Stephan, May 27 2013

Formula

a(n) = Sum_{i = 1..floor(n/2)} i^(n-i).