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A357245 E.g.f. satisfies A(x) * log(A(x)) = 3 * (exp(x) - 1). 1
1, 3, -6, 84, -1599, 42906, -1477716, 62171661, -3090518556, 177237143040, -11518529575857, 836601742598628, -67156626492464064, 5904119985344031639, -564188922815428792914, 58225175660113940932032, -6453955474121138652732903, 764716767229825444834522086 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Lambert W-Function.

FORMULA

a(n) = Sum_{k=0..n} 3^k * (-k+1)^(k-1) * Stirling2(n,k).

E.g.f.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * (3 * (exp(x) - 1))^k / k!.

E.g.f.: A(x) = exp( LambertW(3 * (exp(x) - 1)) ).

E.g.f.: A(x) = 3 * (exp(x) - 1)/LambertW(3 * (exp(x) - 1)).

PROG

(PARI) a(n) = sum(k=0, n, 3^k*(-k+1)^(k-1)*stirling(n, k, 2));

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k+1)^(k-1)*(3*(exp(x)-1))^k/k!)))

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(3*(exp(x)-1)))))

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(3*(exp(x)-1)/lambertw(3*(exp(x)-1))))

CROSSREFS

Cf. A349583, A357244.

Sequence in context: A213138 A349875 A331403 * A157197 A211896 A299433

Adjacent sequences: A357242 A357243 A357244 * A357246 A357247 A357248

KEYWORD

sign

AUTHOR

Seiichi Manyama, Sep 19 2022

STATUS

approved

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Last modified January 29 01:41 EST 2023. Contains 359905 sequences. (Running on oeis4.)