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A109391
a(n) = (n^(n+1))*(n + 1)/2 = A000217(n)*A000312(n).
2
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.
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
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Jun 26 2005
STATUS
approved