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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 A344556 A303175 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 December 2 13:42 EST 2021. Contains 349444 sequences. (Running on oeis4.)