The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A287317 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A287317

Number of 5-dimensional cubic lattice walks that start and end at origin after 2n steps, free to pass through origin at intermediate stages.
(history; published version)

#14 by N. J. A. Sloane at Thu Oct 13 12:46:27 EDT 2022

STATUS

proposed

approved

#13 by Dave R.M. Langers at Thu Oct 13 12:25:19 EDT 2022

STATUS

editing

proposed

#12 by Dave R.M. Langers at Thu Oct 13 12:24:58 EDT 2022

KEYWORD

nonn,nice,easy,walk,changed

#11 by Dave R.M. Langers at Wed Oct 12 11:55:36 EDT 2022

NAME

a(n) = (2*n)! [x^n] BesselI(0, 2*sqrt(x))^5.

Number of 5-dimensional cubic lattice walks that start and end at origin after 2n steps, free to pass through origin at intermediate stages.

FORMULA

a(n) = (2*n)! [x^n] BesselI(0, 2*sqrt(x))^5.

CROSSREFS

Cf. A169714, A287316.

1-4 dimensional analogs are A000984, A002894, A002896, A039699.

KEYWORD

nonn,nice,easy,walk

EXTENSIONS

Moved original definition to formula section and reworded definition descriptively similar to sequence A039699, by Dave R.M. Langers, Oct 12 2022

STATUS

approved

editing

#10 by Vaclav Kotesovec at Mon Nov 13 07:25:53 EST 2017

STATUS

editing

approved

#9 by Vaclav Kotesovec at Mon Nov 13 07:25:48 EST 2017

FORMULA

a(n) ~ 2^(2*n) * 5^(2*n + 5/2) / (16 * Pi^(5/2) * n^(5/2)). - Vaclav Kotesovec, Nov 13 2017

STATUS

approved

editing

#8 by Peter Luschny at Tue May 23 17:57:31 EDT 2017

STATUS

editing

approved

#7 by Peter Luschny at Tue May 23 17:57:25 EDT 2017

FORMULA

a(n) = binomial(2*n,n)*A169714(n).

CROSSREFS

Cf. A169714, A287316.

STATUS

approved

editing

#6 by Peter Luschny at Tue May 23 17:39:02 EDT 2017

STATUS

editing

approved

#5 by Peter Luschny at Tue May 23 17:38:42 EDT 2017

MATHEMATICA

Table[Binomial[2n, n]^2 Sum[(Binomial[n, j]^4/Binomial[2n, 2j]) HypergeometricPFQ[{-j, -j, -j}, {1, 1/2-j}, 1/4], {j, 0, n}], {n, 0, 15}]

STATUS

approved

editing