A363663 - OEIS

A363663

a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-1,n).

1, 4, 11, 46, 127, 596, 1717, 7792, 24806, 108450, 352717, 1563914, 5200301, 22539046, 77876117, 331982444, 1166803111, 4945693769, 17672631901, 74053888812, 269344740908, 1118110015874, 4116715363801, 16984153623296, 63205318063252, 259049084680612

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

FORMULA

a(n) = [x^n] Sum_{k>0} x^k/(1 - k*x^k)^(n+1).

MATHEMATICA

a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n - 1, n] &]; Array[a, 25] (* Amiram Eldar, Jul 12 2023 *)

PROG

(PARI) a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n-1, n));

CROSSREFS

Cf. A167531, A363642, A363645.

Cf. A343548, A363661, A363664.

Sequence in context: A149290 A074410 A359707 * A149291 A149292 A149293

Adjacent sequences: A363660 A363661 A363662 * A363664 A363665 A363666

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 14 2023

STATUS

approved