The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A082030 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A082030

Expansion of e.g.f. exp(x)/(1-x)^3.
(history; published version)

#49 by Harvey P. Dale at Sun Aug 07 17:06:37 EDT 2022

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#48 by Harvey P. Dale at Sun Aug 07 17:06:33 EDT 2022

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[x]/(1-x)^3, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 07 2022 *)

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#47 by Peter Luschny at Tue May 10 15:23:14 EDT 2022

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#46 by Peter Luschny at Tue May 10 15:23:09 EDT 2022

FORMULA

a(n) = KummerU(-n, -n - 2, 1). - Peter Luschny, May 10 2022

MAPLE

a := n -> hypergeom([3, -n], [], -1); seq(round(evalfsimplify(a(n), 100)), n=0..18); # Peter Luschny, Sep 20 2014

seq(simplify(KummerU(-n, -n - 2, 1)), n = 0..20); # Peter Luschny, May 10 2022

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#45 by Susanna Cuyler at Tue Jul 27 21:20:46 EDT 2021

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#44 by Michel Marcus at Tue Jul 27 06:27:38 EDT 2021

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proposed

#43 by Michel Marcus at Tue Jul 27 06:27:35 EDT 2021

FORMULA

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

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#42 by Peter Bala at Tue Jul 27 06:23:41 EDT 2021

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#41 by Peter Bala at Mon Jul 26 13:14:23 EDT 2021

FORMULA

First-order recurrence: P(n-1)*a(n) = n*P(n)*a(n-1) + 1 with a(0) = 1, where P(n) = n^2 + n + 1 = A001564(n). - Peter Bala, Jul 26 2021

CROSSREFS

Cf. A082031, A000522, A001339, A095000, A095177, A096307, A096341, A001564.

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#40 by Joerg Arndt at Tue Jan 21 00:05:57 EST 2020

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proposed

approved