

A074209


Sum of next n terms of the form i^n.


1



2, 25, 405, 8418, 216400, 6668779, 240361121, 9936764996, 463893277176, 24148657338925, 1387253043076813, 87185783860333910, 5951020164442347800, 438417132703015536399, 34673851743509883542625
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OFFSET

1,1


COMMENTS

A rapidly growing sequence. An even more rapidly growing sequence, the sum of next n terms of the form i^i, is given in A074309. Sum of first n terms of the form i^n is A031971. Sum of first n terms of the form i^i is A001923.


LINKS

Table of n, a(n) for n=1..15.


FORMULA

sum(i^n, i=n+1, 2n)


EXAMPLE

a(2) = 25 = 3^2 + 4^2, a(3) = 405 = 4^3 + 5^3 + 6^3, a(4) = 8418 = 5^4 + 6^4 + 7^4 + 8^4, a(5) = 216400 = 6^4 + 7^5 + 8^5 + 9^5 + 10^5.


MATHEMATICA

Table[Sum[i^n, {i, n+1, 2n}], {n, 20}]


CROSSREFS

Cf. A001923, A031971, A074309.
Sequence in context: A270346 A212022 A198710 * A209467 A121252 A322727
Adjacent sequences: A074206 A074207 A074208 * A074210 A074211 A074212


KEYWORD

nonn


AUTHOR

Zak Seidov, Sep 22 2002


STATUS

approved



