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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 Index entries for linear recurrences with constant coefficients, signature (462, -91531, 10359990, -751926160, 37211988696, -1302889937812, 33041329661136, -616216166660230, 8532037831808700, -88161849837783250, 681071135526667500, -3928678356172712500, 16849648606559250000, -53333569862180312500, 123260625734287500000, -205051485813712890625, 240815404573652343750, -193749765819873046875, 101292345769042968750, -30943180590820312500, 4187798876953125000). 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 February 29 15:41 EST 2024. Contains 370425 sequences. (Running on oeis4.)