A377664 - OEIS

%I #7 Nov 14 2024 17:55:59

%S 1,0,-3,46,497,-47524,-737891,218380506,4534099905,-3027853088648,

%T -79034002960099,99913537539058310,3145444161956190577,

%U -6725392006687056786732,-248035037340684934103427,829076907459643714597871026,35061737998144136797680434945,-172868475620109085260017037166096

%N a(n) = Sum_{j=0..n} binomial(n, j)*Euler(j, 0)*(2*n)^j. Main diagonal of A377666.

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

%p seq(a(n), n = 0..16);

%t a[0] := 1; a[n_] := Sum[Binomial[n, j] EulerE[j, 0] (2n)^j, {j, 0, n}];

%t Table[a[n], {n, 0, 16}]

%o (Python)

%o from math import comb

%o from sympy import euler

%o def A377664(n): return sum(comb(n,j)*euler(j,0)*(n<<1)**j for j in range(n+1)) # _Chai Wah Wu_, Nov 14 2024

%Y Cf. A377666.

%K sign

%O 0,3

%A _Peter Luschny_, Nov 14 2024