A394443 - OEIS

%I #9 Apr 28 2026 17:59:30

%S 1,2,14,156,2404,47310,1133362,32005400,1041071208,38332962810,

%T 1576117028870,71578863309492,3558526264337420,192218569184875142,

%U 11210020924481677690,702004358782658232240,46983434611147824097104,3346765071252016227670386,252810562072190606804106894

%N a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(k - j) * binomial(k, j) * j^n * 2^j.

%H Alois P. Heinz, <a href="/A394443/b394443.txt">Table of n, a(n) for n = 0..362</a>

%F a(n) = Sum_{k=0..n} A394444(n, k).

%p a := n -> local j, k; add(add((-1)^(k-j)*binomial(k, j)*j^n*2^j, j = 0..k), k = 0..n): seq(a(n), n = 0..18);

%p # Alternative:

%p b:= proc(n, k) option remember;

%p      `if`(n=0, 1, k*(b(n-1, k)+b(n-1, k-1)))

%p     end:

%p a:= n-> add(b(n, k), k=0..n):

%p seq(a(n), n=0..18);  # _Alois P. Heinz_, Apr 28 2026

%Y Cf. A394444.

%K nonn

%O 0,2

%A _Peter Luschny_, Mar 20 2026