The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A251585

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A251585

a(n) = 5^(n-3) * (n+1)^(n-5) * (16*n^3 + 87*n^2 + 172*n + 125).
(history; published version)

#12 by Charles R Greathouse IV at Thu Sep 08 08:46:10 EDT 2022

PROG

(MAGMAMagma) [5^(n - 3)*(n + 1)^(n - 5)*(16*n^3 + 87*n^2 + 172*n + 125): n in [0..50]]; // G. C. Greubel, Nov 13 2017

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#11 by Bruno Berselli at Tue Nov 14 03:05:03 EST 2017

STATUS

reviewed

approved

#10 by Michel Marcus at Tue Nov 14 00:32:26 EST 2017

STATUS

proposed

reviewed

#9 by Jon E. Schoenfield at Tue Nov 14 00:25:36 EST 2017

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Tue Nov 14 00:25:32 EST 2017

EXAMPLE

E.g.f.: A(x) = 1 + x + 7*x^2/2! + 116*x^3/3! + 3229*x^4/4! + 129000*x^5/5! + ...

G(x) = 1 + x + 5*x^2 + 35*x^3 + 285*x^4 + 2530*x^5 + 23751*x^6 + ...

F(x) = 1 + x + 5*x^2/2! + 65*x^3/3! + 1505*x^4/4! + 51505*x^5/5! + ...

STATUS

proposed

editing

#7 by G. C. Greubel at Tue Nov 14 00:13:17 EST 2017

STATUS

editing

proposed

#6 by G. C. Greubel at Tue Nov 14 00:12:40 EST 2017

LINKS

G. C. Greubel, <a href="/A251585/b251585.txt">Table of n, a(n) for n = 0..312</a>

MATHEMATICA

Table[5^(n - 3)*(n + 1)^(n - 5)*(16*n^3 + 87*n^2 + 172*n + 125), {n, 0, 50}] (* G. C. Greubel, Nov 13 2017 *)

PROG

(MAGMA) [5^(n - 3)*(n + 1)^(n - 5)*(16*n^3 + 87*n^2 + 172*n + 125): n in [0..50]]; // G. C. Greubel, Nov 13 2017

STATUS

approved

editing

#5 by Vaclav Kotesovec at Sun Dec 07 10:16:19 EST 2014

STATUS

editing

approved

#4 by Vaclav Kotesovec at Sun Dec 07 10:15:51 EST 2014

NAME

a(n) = 5^(n-3) * (n+1)^(n-5) * (16*n^3 + 87*n^2 + 172*n + 125).

FORMULA

Let G(x) = 1 + x*G(x)^5 be the g.f. of A002294, then the e.g.f. A(x) of this sequence satisfies:

E.g.f.: -LambertW(-5*x) * (5 + LambertW(-5*x))^4 / (x*5^5). - Vaclav Kotesovec, Dec 07 2014

EXAMPLE

E.g.f.: A(x) = 1 + x + 7*x^2/2! + 116*x^3/3! + 3229*x^4/4! + 129000*x^5/5! +...

PROG

(PARI) {a(n) = 5^(n-3) * (n+1)^(n-5) * (16*n^3 + 87*n^2 + 172*n + 125)}

CROSSREFS

Cf. A251575, A002294.

STATUS

approved

editing

#3 by Paul D. Hanna at Sat Dec 06 15:27:04 EST 2014

STATUS

editing

approved