A367808 -id:A367808 - cp's OEIS frontend

A367809 a(n) = Sum_{k=0..n} A011971(n, k) * (-2)^(n - k).

1, 0, 7, -17, 166, -931, 8333, -67902, 668341, -6733957, 74909152, -875130273, 10931723505, -143624036492, 1989841289619, -28881136161245, 438657928012966, -6948176832355895, 114571387874994353, -1962292996833874918, 34849770255925089153, -640681440719312240225, 12174584322610783966760

Offset: 0

Peter Luschny, Dec 01 2023

sign

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

Cf. A011971, A367808.

# Using the function b from A367808.
def a(n): return sum(b(n)[k] * (-2) ** (n - k) for k in range(n + 1))
print([a(n) for n in range(23)])

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

A367809 a(n) = Sum_{k=0..n} A011971(n, k) * (-2)^(n - k).

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