A302178 The number of 3D walks of semilength n in a quadrant returning to the origin.

1, 4, 40, 570, 9898, 195216, 4209084, 96941130, 2349133930, 59272544760, 1545550116240, 41416083787260, 1135679731004700, 31760915181412800, 903492759037272480, 26086451983000501410, 763124703525758894490, 22585374873810849150600, 675419388009799152812400

Offset: 0

Author

N. J. A. Sloane, Apr 09 2018

Keywords

• nonn
• walk

Links

• Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5. The sequence is type aab in Table 3.

Crossrefs

Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814.

Formula

a(n) = Sum_{i=0..n,j=0..n-i} A000108(i) * A000108(j) * A000984_(n-i-j) * (2n)!/((2i)!*(2j)!*(2n-2i-2j)!). - Nachum Dershowitz, Aug 13 2020

Extensions

a(8)-a(18) from Nachum Dershowitz, Aug 03 2020

Name edited by Nachum Dershowitz, Aug 13 2020