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A255806 E.g.f.: exp(Sum_{k>=1} 3*x^k). 5
1, 3, 15, 99, 801, 7623, 83079, 1017495, 13808097, 205374123, 3318673599, 57845821707, 1081091446785, 21553820597871, 456410531639799, 10225931132021247, 241609515712343361, 6002109578246918355, 156360266121378584943, 4261404847790207796147 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, if e.g.f. = exp(Sum_{k>=1} m*x^k) = exp(m*x/(1-x)) and m>0, then a(n) ~ n! * m^(1/4) * exp(2*sqrt(m*n) - m/2) / (2 * sqrt(Pi) * n^(3/4)).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..435

FORMULA

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

a(n) ~ 3^(1/4) * exp(2*sqrt(3*n) - 3/2) * n! / (2*sqrt(Pi)*n^(3/4)).

a(n) = (2*n+1)*a(n-1) - (n-2)*(n-1)*a(n-2). - Vaclav Kotesovec, Nov 04 2016

MATHEMATICA

nmax=20; CoefficientList[Series[Exp[Sum[3*x^k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!

CoefficientList[Series[E^(3*x/(1-x)), {x, 0, 20}], x] * Range[0, 20]!

PROG

(PARI) x= 'x + O('x^50); Vec(serlaplace(exp(3*x/(1-x)))) \\ G. C. Greubel, Feb 05 2017

CROSSREFS

Cf. A000262, A052897.

Sequence in context: A111546 A219359 A152402 * A226515 A135883 A147664

Adjacent sequences:  A255803 A255804 A255805 * A255807 A255808 A255809

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Mar 07 2015

STATUS

approved

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Last modified September 22 17:13 EDT 2019. Contains 327311 sequences. (Running on oeis4.)