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A349969 a(n) = Sum_{k=0..n} (k*n)^(n-k). 3
1, 1, 3, 16, 141, 1871, 34951, 873174, 27951929, 1107415549, 52891809491, 2987861887924, 196828568831365, 14950745148070499, 1296606974501951743, 127238563043551898986, 14012626653816435643633, 1719136634276882827095009, 233448782800118609096218891 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..284

FORMULA

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

a(n) ~ sqrt(2*Pi/(n*(1 + LambertW(exp(1)*n^2)))) * (n^2/LambertW(exp(1)*n^2))^(n + 1/2 - n/LambertW(exp(1)*n^2)). - Vaclav Kotesovec, Dec 07 2021

MATHEMATICA

a[n_] := Sum[If[k == n == 0, 1, (k*n)^(n - k)], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 07 2021 *)

PROG

(PARI) a(n) = sum(k=0, n, (k*n)^(n-k));

CROSSREFS

Cf. A026898, A155956, A349964, A349970.

Sequence in context: A020554 A062874 A321239 * A109398 A294003 A006058

Adjacent sequences: A349966 A349967 A349968 * A349970 A349971 A349972

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 07 2021

STATUS

approved

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Last modified February 7 02:40 EST 2023. Contains 360111 sequences. (Running on oeis4.)