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A109391 (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 (list; graph; refs; listen; history; text; internal format)
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,...,n} occurs n^(n-1) times in each of the n positions of the n^n sequences and (1+...+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 * A138455 A024221 A093152

Adjacent sequences:  A109388 A109389 A109390 * A109392 A109393 A109394

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Jun 26 2005

STATUS

approved

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Last modified May 26 18:26 EDT 2017. Contains 287129 sequences.