A363401 - OEIS

%I #7 Jun 02 2023 08:39:37

%S 1,5,68,302,33104,64272,43575104,30313712,111402371328,25258008320,

%T 468857355838464,32779942009344,2941165554120118272,61149815860711424,

%U 25734702989598729256960,155090406558662064128,299529317622247725531725824,513370937392454603833344

%N 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.

%F 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

%p 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);

%t 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 *)

%Y Cf. A363400.

%K nonn

%O 0,2

%A _Peter Luschny_, Jun 02 2023