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A357727 Expansion of e.g.f. cos( 2 * (exp(x) - 1) ). 3
1, 0, -4, -12, -12, 100, 852, 4004, 9940, -36828, -726316, -6174300, -35968812, -109708508, 702818004, 16677814436, 188794428628, 1542659688996, 8359981681364, -3068614764636, -868989327994668, -15076627082974940, -179727483880747308 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

Eric Weisstein's MathWorld, Bell Polynomial.

FORMULA

a(n) = Sum_{k=0..floor(n/2)} (-4)^(k) * Stirling2(n,2*k).

a(n) = 1; a(n) = -4 * Sum_{k=0..n-1} binomial(n-1, k) * A357738(k).

a(n) = ( Bell_n(2 * i) + Bell_n(-2 * i) )/2, where Bell_n(x) is n-th Bell polynomial and i is the imaginary unit.

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(cos(2*(exp(x)-1))))

(PARI) a(n) = sum(k=0, n\2, (-4)^k*stirling(n, 2*k, 2));

(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);

a(n) = round((Bell_poly(n, 2*I)+Bell_poly(n, -2*I)))/2;

CROSSREFS

Column k=4 of A357728.

Cf. A065143, A357719, A357738.

Sequence in context: A202636 A239194 A355801 * A009115 A051434 A074138

Adjacent sequences: A357724 A357725 A357726 * A357728 A357729 A357730

KEYWORD

sign

AUTHOR

Seiichi Manyama, Oct 10 2022

STATUS

approved

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Last modified February 3 02:45 EST 2023. Contains 360024 sequences. (Running on oeis4.)