A109391 a(n) = (n^(n+1))*(n + 1)/2 = A000217(n)*A000312(n).

0, 1, 12, 162, 2560, 46875, 979776, 23059204, 603979776, 17433922005, 550000000000, 18830570260326, 695455834963968, 27561634699895023, 1166760716683591680, 52547266845703125000, 2508757194024499019776

Offset

0,3

Comments

The sum of all the terms of all A000312(n) sequences having exactly n terms all chosen from {1,2,...,n}. Partial sums are A109392.

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (n^(n+1))*(n + 1)/2.

Example

a(2) = (2^(2+1))*(2 + 1)/2 = 8*3/2 = 12. Note that the 2^2 sequences 1, 1; 1, 2; 2, 1; 2, 2 have 1 + 1 + 1 + 2 + 2 + 1 + 2 + 2 = 12 as the sum of all their terms (each element of {1, 2, ... , n} occurs n^(n-1) times in each of the n positions of the n^n sequences and (1 + 2 + ... + n)*n*n^(n-1) = A000217(n)*A000312(n)).

Crossrefs

Cf. A000217 (triangular numbers), A000312 (n^n: endofunctions), A109392 (partial sums).

Sequence in context: A048609 A048603 A275040 * A296194 A307071 A138455

Adjacent sequences: A109388 A109389 A109390 * A109392 A109393 A109394

Keyword

nonn

Author

Rick L. Shepherd, Jun 26 2005

Status

approved