A002750 Sum of logarithmic numbers.

1, 4, 15, 76, 373, 2676, 17539, 152860, 1383561, 14658148, 143131351, 2070738924, 24754959805, 341745565396, 5260157782923, 92358395065276, 1377499388715409, 27622124789948100, 476285499100204831, 10464946811144407948, 222724531608924013701

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Robert Israel, Table of n, a(n) for n = 0..447
• J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]
• Index entries for sequences related to logarithmic numbers

Crossrefs

Cf. A000203.

Programs

Maple

a:= n-> n!*add(numtheory[sigma](m+1)/(n-m)!, m=0..n):
seq(a(n), n=0..22);  # Alois P. Heinz, Sep 16 2021

Mathematica

a[n_] := n!*Sum[DivisorSigma[1, m+1]/(n-m)!, {m, 0, n}];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Nov 19 2024, after Alois P. Heinz *)

Formula

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

Extensions

More terms from Jeffrey Shallit

More terms from Vladeta Jovovic, Feb 08 2003