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A151643 Number of permutations of 4 indistinguishable copies of 1..n with exactly 5 adjacent element pairs in decreasing order. 2
0, 0, 8464, 15018688, 6501577152, 1585757994496, 290861341616496, 45679059507623040, 6563622028755987104, 895009629522636673728, 118277136569294999638992, 15337783893522951844828992, 1966328218272794506172178816, 250347808250994150312231611520 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

G. C. Greubel, Generating functions and recurrence

FORMULA

From G. C. Greubel, Sep 10 2022: (Start)

a(n) = Sum_{j=0..5} (-1)^j*binomial(4*n+1, j)*binomial(9-j, 4)^n.

G.f., e.g.f., and recurrence are in the file "Generating functions and recurrence". (End)

MATHEMATICA

Table[Sum[(-1)^j*Binomial[4*n+1, j]*Binomial[9-j, 4]^n, {j, 0, 5}], {n, 30}] (* G. C. Greubel, Sep 10 2022 *)

PROG

(Magma) [(&+[(-1)^j*Binomial(4*n+1, j)*Binomial(9-j, 4)^n: j in [0..5]]): n in [1..30]]; // G. C. Greubel, Sep 10 2022

(SageMath)

def A151643(n): return sum((-1)^j*binomial(4*n+1, j)*binomial(9-j, 4)^n for j in (0..5))

[A151643(n) for n in (1..30)] # G. C. Greubel, Sep 10 2022

CROSSREFS

Column k=5 of A236463.

Sequence in context: A170787 A237846 A232907 * A031590 A322160 A253499

Adjacent sequences:  A151640 A151641 A151642 * A151644 A151645 A151646

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 29 2009

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, May 06 2020

STATUS

approved

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Last modified October 5 20:00 EDT 2022. Contains 357261 sequences. (Running on oeis4.)