The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A328725 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A328725

Constant term in the expansion of (1 + x + y + z + 1/x + 1/y + 1/z + x*y + y*z + z*x + 1/(x*y) + 1/(y*z) + 1/(z*x) + x*y*z + 1/(x*y*z))^n.
(history; published version)

#37 by Susanna Cuyler at Sat May 16 14:26:15 EDT 2020

STATUS

proposed

approved

#36 by Andrew Howroyd at Sat May 16 13:15:12 EDT 2020

STATUS

editing

proposed

#35 by Andrew Howroyd at Sat May 16 13:11:23 EDT 2020

CROSSREFS

Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^m: A002426 (m=2), A208446 A172634 (m=3), this sequence (m=4), A328750 (m=5).

STATUS

approved

editing

Discussion

Sat May 16

13:15

Andrew Howroyd: Replacing ref to A208446 with A172634 since the former is a duplicate.

#34 by Vaclav Kotesovec at Mon Oct 28 07:52:30 EDT 2019

STATUS

editing

approved

#33 by Vaclav Kotesovec at Mon Oct 28 07:51:42 EDT 2019

FORMULA

From Vaclav Kotesovec, Oct 28 2019: (Start)

Recurrence: n^3*a(n) = (2*n - 1)^3*a(n-1) + (n-1)*(94*n^2 - 188*n + 93)*a(n-2) + 80*(n-2)*(n-1)*(2*n - 3)*a(n-3) + 75*(n-3)*(n-2)*(n-1)*a(n-4).

a(n) ~ 15^(n + 3/2) / (2^(11/2) * Pi^(3/2) * n^(3/2)). (End)

STATUS

approved

editing

#32 by Alois P. Heinz at Sun Oct 27 13:36:44 EDT 2019

STATUS

proposed

approved

#31 by Seiichi Manyama at Sun Oct 27 13:32:38 EDT 2019

STATUS

editing

proposed

#30 by Seiichi Manyama at Sun Oct 27 13:32:28 EDT 2019

CROSSREFS

Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^m: A002426 (m=2), A208446 (m=3), this sequence (m=4), A328750 (m=5).

#29 by Seiichi Manyama at Sun Oct 27 13:32:06 EDT 2019

CROSSREFS

Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^m: A002426 (m=2), A208446 (m=3), this sequence (m=4).,

STATUS

proposed

editing

#28 by Seiichi Manyama at Sun Oct 27 13:31:09 EDT 2019

STATUS

editing

proposed