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A354519

Expansion of e.g.f. exp(x) * log(sec(x)).

0, 1, 3, 8, 20, 61, 203, 888, 4080, 24001, 140283, 1028048, 7248020, 63374221, 522164243, 5299033488, 49924707840, 576514338721, 6110861416083, 79100066353208, 931434877343540, 13355627237749501, 172948115797623803, 2720827878727067208, 38424408320191299120

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..25.

FORMULA

a(n) = Sum_{k=1..floor(n/2)} A000182(k) * binomial(n,2*k).

a(n) ~ 2^(n + 1/2) * (exp(Pi/2) + (-1)^n/exp(Pi/2)) * n^(n - 1/2) / (Pi^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Aug 17 2022

PROG

(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(exp(x)*log(1/cos(x)))))

(PARI) a(n) = sum(k=1, n\2, ((-4)^k-(-16)^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));

(Python)