A367808 a(n) = Sum_{k=0..n} A011971(n, k) * 2^(n - k).

1, 4, 19, 103, 634, 4393, 33893, 288158, 2674849, 26888251, 290614732, 3356438587, 41203019361, 535141595208, 7324289215167, 105271669493307, 1584113665608394, 24890073684310405, 407378999173905545, 6930779764599424550, 122334506551009552893, 2236412875771806004767

Offset

0,2

Comments

The Peirce/Aitken polynomials evaluated at 1/2 and the result normalized with 2^n.

Links

Table of n, a(n) for n=0..21.

Prog

(Python)
from functools import cache
@cache
def b(n: int) -> list[int]:
    if n == 0: return [1]
    row = [b(n - 1)[n - 1]] + b(n - 1)
    for k in range(1, n + 1): row[k] += row[k - 1]
    return row
def a(n): return sum(b(n)[k] * 2 ** (n - k) for k in range(n + 1))
print([a(n) for n in range(22)])

Crossrefs

Cf. A011971, A367809.

Keyword

nonn

Author

Peter Luschny, Dec 01 2023

Status

approved