A363401 a(n) = Sum_{k=0..n} 2^(n - k) * Sum_{j=0..k} binomial(k, j) * ((2 - (n mod 2)) * j + 1)^n. Row sums of A363400.

1, 5, 68, 302, 33104, 64272, 43575104, 30313712, 111402371328, 25258008320, 468857355838464, 32779942009344, 2941165554120118272, 61149815860711424, 25734702989598729256960, 155090406558662064128, 299529317622247725531725824, 513370937392454603833344

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) ~ sqrt(1 + LambertW(exp(-1))) * (2-mod(n,2))^n * n^n / ((1 - LambertW(exp(-1))) * exp(n) * LambertW(exp(-1))^(n + 1/(2-mod(n,2)))). - Vaclav Kotesovec, Jun 02 2023

Maple

a := n -> add(add(binomial(k, j) * ((2 - irem(n, 2)) * j + 1)^n, j = 0..k) * 2^(n - k), k = 0..n): seq(a(n), n = 0..17);

Mathematica

Table[Sum[2^(n-k) * Sum[Binomial[k, j]*((2 - Mod[n, 2])*j + 1)^n, {j, 0, k}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 02 2023 *)

Crossrefs

Cf. A363400.

Sequence in context: A252794 A328359 A003361 * A336433 A099334 A281558

Adjacent sequences: A363398 A363399 A363400 * A363402 A363403 A363404

Keyword

nonn

Author

Peter Luschny, Jun 02 2023

Status

approved