A151644 Number of permutations of 4 indistinguishable copies of 1..n with exactly 6 adjacent element pairs in decreasing order.

0, 0, 1828, 21571984, 29066972368, 16938467955200, 6501926870387116, 1978065945844840160, 524378714083391626872, 127734445724723139679472, 29503552588857666326833140, 6587452899587031432766113392, 1439127765510353092008927027552, 310010313330353917185364216860320

Offset: 1

Author

R. H. Hardin, May 29 2009

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• G. C. Greubel, Generating functions and recurrence
• Index entries for linear recurrences with constant coefficients, signature (924, -378521, 91617024, -14722624611, 1672843754916, -139720634979999, 8802985293454896, -425959267257617574, 16033075393526507736, -473719205662776457290, 11056881154552526304000, -204722830335985725627750, 3014129978676701732565000, -35317513927339931248518750, 329166550817222634139500000, -2435724534109739934786328125, 14263842696601765936879687500, -65800836590491435623611328125, 237643329148874488008750000000, -666631524934449548464990234375, 1438281882495029477739257812500, -2357806371916471525008544921875, 2891080516482183085839843750000, -2594002250018865048706054687500, 1646666887498820332031250000000, -698563762562096740722656250000, 177368526026876953125000000000, -20361182834718017578125000000).

Crossrefs

Column k=6 of A236463.

Programs

Magma

[(&+[(-1)^j*Binomial(4*n+1, j)*Binomial(10-j, 4)^n: j in [0..6]]): n in [1..30]]; // G. C. Greubel, Sep 12 2022

Mathematica

Table[Sum[(-1)^j*Binomial[4*n+1, j]*Binomial[10-j, 4]^n, {j,0,6}], {n, 30}] (* G. C. Greubel, Sep 12 2022 *)

SageMath

def A151644(n): return sum((-1)^j*binomial(4*n+1, j)*binomial(10-j, 4)^n for j in (0..6))
[A151644(n) for n in (1..30)] # G. C. Greubel, Sep 12 2022

Formula

From G. C. Greubel, Sep 12 2022: (Start)

a(n) = Sum_{j=0..6} (-1)^j*binomial(4*n+1, j)*binomial(10-j, 4)^n.

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

Extensions

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