A068476 a(n) = Sum_{m=1..n} m*n^(m+(-1)^n).

0, 1, 20, 34, 5008, 3711, 1948356, 937924, 1205220416, 429794605, 1098765432100, 310989720966, 1390027428561168, 326011399456939, 2332600912091693348, 466937872906120456, 5016202619581534249216, 875711370981239308953

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..385

Formula

If n >= 2, a(n) = n^(1+(-1)^n)*(n^n*(n^2-n-1)+1)/(n-1)^2. - Robert Israel, Nov 15 2017

Example

a(2) = 2^(1+1)+2*2^(2+1) = 4+16 = 20.

Maple

b := n->sum(m*n^(m+(-1)^n), m=1..n);
# Alternative:
f:= n -> n^(1+(-1)^n)*(n^n*(n^2-n-1)+1)/(n-1)^2:
f(0):= 0: f(1):= 1:
map(f, [$0..40]);

Mathematica

Table[Sum[m*n^(m+(-1)^n), {m, 1, n}], {n, 0, 30}] (* G. C. Greubel, Oct 13 2018 *)

Prog

(PARI) a(n) = sum(m=1, n, m*n^(m+(-1)^n)); \\ Michel Marcus, Nov 15 2017
(Magma) [0] cat [(&+[m*n^(m+(-1)^n): m in [1..n]]): n in [1..30]]; // G. C. Greubel, Oct 13 2018

Crossrefs

Cf. A062806 (without the (-1)^n).

Sequence in context: A043946 A160937 A060124 * A003895 A157426 A325603

Adjacent sequences: A068473 A068474 A068475 * A068477 A068478 A068479

Keyword

nonn

Author

Francois Jooste (phukraut(AT)hotmail.com), Mar 10 2002

Status

approved