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Sum of logarithmic numbers.
(Formerly M3506 N1422)
2

%I M3506 N1422 #27 Oct 20 2023 09:39:50

%S 1,4,15,76,373,2676,17539,152860,1383561,14658148,143131351,

%T 2070738924,24754959805,341745565396,5260157782923,92358395065276,

%U 1377499388715409,27622124789948100,476285499100204831,10464946811144407948,222724531608924013701

%N Sum of logarithmic numbers.

%D J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. M. Gandhi, <a href="/A002741/a002741.pdf">On logarithmic numbers</a>, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]

%H <a href="/index/Lo#logarithmic">Index entries for sequences related to logarithmic numbers</a>

%F E.g.f.: F(x)/x*exp(x) where F(x) is o.g.f. for A000203(). a(n) = Sum_{m=1..n+1} A000203(m)*binomial(n, m-1)*(m-1)!. - _Vladeta Jovovic_, Feb 08 2003

%p a:= n-> n!*add(numtheory[sigma](m+1)/(n-m)!, m=0..n):

%p seq(a(n), n=0..22); # _Alois P. Heinz_, Sep 16 2021

%Y Cf. A000203.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Jeffrey Shallit_

%E More terms from _Vladeta Jovovic_, Feb 08 2003