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Revision History for A361283

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Showing entries 1-10 | older changes

A361283

Expansion of e.g.f. exp(x/(1-x)^4).
(history; published version)

#17 by Vaclav Kotesovec at Sat Nov 11 10:16:22 EST 2023

STATUS

editing

approved

#16 by Vaclav Kotesovec at Sat Nov 11 10:16:14 EST 2023

FORMULA

a(n) ~ 2^(1/5) * n^(n - 1/10) * exp(-27/1280 - 13*2^(3/5)*n^(1/5)/800 + 13*2^(1/5)*n^(2/5)/240 + 2^(-6/5)*n^(3/5) + 5*2^(-8/5)*n^(4/5) - n) / sqrt(5) * (1 + 116303*2^(12/5)/(3200000*n^(1/5))). - Vaclav Kotesovec, Nov 11 2023

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approved

editing

#15 by R. J. Mathar at Sun Mar 12 09:58:05 EDT 2023

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editing

approved

#14 by R. J. Mathar at Sun Mar 12 09:58:00 EDT 2023

FORMULA

D-finite with recurrence a(n) +(-5*n+4)*a(n-1) +(n-1)*(10*n-23)*a(n-2) -10*(n-1)*(n-2)*(n-3)*a(n-3) +5*(n-1)*(n-2)*(n-3)*(n-4)*a(n-4) -(n-5)*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Mar 12 2023

MAPLE

A361283 := proc(n)

n!*add(binomial(n+3*k-1, n-k)/k!, k=0..n) ;

end proc:

seq(A361283(n), n=0..40) ; # R. J. Mathar, Mar 12 2023

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approved

editing

#13 by Alois P. Heinz at Wed Mar 08 07:45:57 EST 2023

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proposed

approved

#12 by Seiichi Manyama at Wed Mar 08 06:33:07 EST 2023

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proposed

#11 by Seiichi Manyama at Wed Mar 08 06:31:43 EST 2023

LINKS

Seiichi Manyama, <a href="/A361283/b361283.txt">Table of n, a(n) for n = 0..414</a>

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approved

editing

#10 by Michael De Vlieger at Tue Mar 07 10:37:30 EST 2023

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proposed

approved

#9 by Seiichi Manyama at Tue Mar 07 08:18:13 EST 2023

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editing

proposed

#8 by Seiichi Manyama at Tue Mar 07 08:13:00 EST 2023

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^4)))