A367809 -id:A367809 - cp's OEIS frontend

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

Peter Luschny, Dec 01 2023

nonn

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

Cf. A011971, A367809.

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)])

A367775 a(n) = Sum_{k=0..n} (-1)^(n - k) * A011971(n, k).

Original entry on oeis.org

1, 1, 4, 7, 37, 94, 587, 1925, 13606, 54217, 424381, 1979704, 16918869, 90086877, 831972372, 4964577987, 49154794969, 324183365662, 3419501188439, 24655458609377, 275624716500750, 2153735319395661, 25406228456463665, 213606545948092304, 2649077873736448473

Offset: 0

Peter Luschny, Dec 02 2023

nonn

Alternating row sums of the Peirce/Aitken/Bell triangle A011971.

Cf. A011971, A005493, A367808, A367809.

# Using the function b from A367808.
def a(n): return sum(b(n)[k] * (-1)**(n - k) for k in range(n + 1))
print([a(n) for n in range(25)])

cp's OEIS Frontend

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

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