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URL: https://oeis.org/A354520

⇱ A354520 - OEIS

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A354520
Expansion of e.g.f. exp(x) * log(cosh(x)).
5
0, 1, 3, 4, 0, 1, 63, 64, -1320, -1319, 49203, 49204, -2653560, -2653559, 196707423, 196707424, -19194804720, -19194804719, 2385684870723, 2385684870724, -367985503366800, -367985503366799, 68980888889771103, 68980888889771104, -15445553274667315800
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{k=1..floor(n/2)} (-1)^(k+1) * A000182(k) * binomial(n,2*k).
a(2*n) = a(2*n-1) + 1.
PROG
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(exp(x)*log(cosh(x)))))
(PARI) a(n) = sum(k=1, n\2, (16^k-4^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));
(Python)
from math import comb
from sympy import bernoulli
def A354520(n): return sum((((2<<(m:=k<<1))-2)*bernoulli(m)<<m-2)//k*comb(n, k<<1) for k in range(1, (n>>1)+1)) # Chai Wah Wu, Apr 15 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 16 2022
STATUS
approved