A377664 a(n) = Sum_{j=0..n} binomial(n, j)*Euler(j, 0)*(2*n)^j. Main diagonal of A377666.

1, 0, -3, 46, 497, -47524, -737891, 218380506, 4534099905, -3027853088648, -79034002960099, 99913537539058310, 3145444161956190577, -6725392006687056786732, -248035037340684934103427, 829076907459643714597871026, 35061737998144136797680434945, -172868475620109085260017037166096

Offset: 0

Author

Peter Luschny, Nov 14 2024

Keywords

• sign

Crossrefs

Cf. A377666.

Programs

Maple

a := n -> local j; add(binomial(n, j)*euler(j, 0)*(2*n)^j, j = 0..n):
seq(a(n), n = 0..16);

Mathematica

a[0] := 1; a[n_] := Sum[Binomial[n, j] EulerE[j, 0] (2n)^j, {j, 0, n}];
Table[a[n], {n, 0, 16}]

Python

from math import comb
from sympy import euler
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