A358652 - OEIS

A358652

a(n) = n!*Sum_{m=1..floor((n+1)/2)} 1/(m*binomial(n-m,m-1)).

1, 2, 9, 30, 180, 890, 7084, 47544, 478512, 4103712, 50079744, 525568032, 7531512768, 93697680960, 1539661512960, 22172241784320, 410427317468160, 6717998786595840, 138197449498521600, 2534644598027673600, 57329127350795059200

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

E.g.f.: log(1-x)/x/(1-x)+(-(-1+x)*(1+2*x))*log((1-x)^2*(1+x))/(x*(x^2-x-1)*(1-x))+(li[2](x*((1-x)*x+1))-li[2](x))/(1-x)^2.

MATHEMATICA

a[n_] := n! * Sum[1/(m*(Binomial[n - m, m - 1])), {m, 1, Floor[(n + 1)/2]}]; Array[a, 21] (* Amiram Eldar, Nov 25 2022 *)

PROG

(Maxima)

a(n):=n!*sum(1/(m*(binomial(n-m, m-1))), m, 1, floor((n+1)/2));

(PARI) a(n) = n!*sum(m=1, (n+1)\2, 1/(m*binomial(n-m, m-1))); \\ Michel Marcus, Nov 25 2022

CROSSREFS

Sequence in context: A181954 A343565 A318101 * A347893 A151823 A084652

Adjacent sequences: A358649 A358650 A358651 * A358653 A358654 A358655

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Nov 25 2022

STATUS

approved