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

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

Index entries for sequences related to partitions

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A226140.

Sequence in context: A110421 A176751 A123822 * A321718 A304127 A220518

Adjacent sequences: A226062 A226063 A226064 * A226066 A226067 A226068

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 24 2013

Status

approved