A002750 Sum of logarithmic numbers. (Formerly M3506 N1422)

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

Offset

0,2

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

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

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 *)

Crossrefs

Cf. A000203.

Sequence in context: A032270 A198057 A263004 * A178887 A002467 A332652

Adjacent sequences: A002747 A002748 A002749 * A002751 A002752 A002753

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jeffrey Shallit

More terms from Vladeta Jovovic, Feb 08 2003

Status

approved