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A068475 a(n) = Sum_{m=0..n} m*n^(m-1). 3
0, 1, 5, 34, 313, 3711, 54121, 937924, 18831569, 429794605, 10987654321, 310989720966, 9652968253897, 326011399456939, 11901025061692313, 466937872906120456, 19594541482740368161, 875711370981239308953 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The closed form comes from taking the derivative of the closed form of A031972, for which each term of this sequence is a derivative. - Jonas Whidden, Oct 18 2011

a(n) = A062806(n) / n. - Reinhard Zumkeller, Nov 22 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..250

FORMULA

a(1)=1. For n>1, a(n) = ((n-1)*(n+1)*n^n - n^(n+1) + 1)/(n-1)^2. - Jonas Whidden, Oct 18 2011

EXAMPLE

a(2)=sum(m*2^(m-1),m=1..2)=1+2*2=5.

MAPLE

a := n->sum(m*n^(m-1), m=1..n);

MATHEMATICA

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

PROG

(Haskell)

a068475 n = sum $ zipWith (*) [1..n] $ iterate (* n) 1

-- Reinhard Zumkeller, Nov 22 2014

(PARI) for(n=0, 30, print1(if(n==0, 0, sum(m=0, n, m*n^(m-1))), ", ")) \\ G. C. Greubel, Oct 13 2018

(MAGMA) [0] cat [(&+[m*n^(m-1): m in [0..n]]): n in [1..30]]; // G. C. Greubel, Oct 13 2018

CROSSREFS

Derivative sequence of A031972.

Cf. A062806, A113630.

Sequence in context: A121323 A328488 A258179 * A097817 A303175 A197714

Adjacent sequences:  A068472 A068473 A068474 * A068476 A068477 A068478

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified September 19 20:55 EDT 2020. Contains 337182 sequences. (Running on oeis4.)