A151630 Number of permutations of 2 indistinguishable copies of 1..n with exactly 8 adjacent element pairs in decreasing order.

0, 0, 0, 0, 1, 37257, 49258935, 19323413187, 3950966047950, 539417838175698, 56160822639510114, 4828612774471173450, 360918591663105680031, 24285778099889122541071, 1507815882167268489272385, 87937588306397361416746005, 4882223035755085016119166100

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
• Index entries for linear recurrences with constant coefficients, signature (495, -117117, 17647773, -1903962060, 156757247010, -10251395632590, 547263937214190, -24324431827594815, 913604942997437285, -29330261021755017639, 812145644279366953815, -19536467308476604835118, 410659658077014965566332, -7578696975148131792068340, 123267861018665262572785476, -1772533955817200772006505695, 22589412092760272526249081417, -255637202218592552368928158843, 2572704107472364912183081654395, -23049204197252732334976831299504, 183953147111817401024161390520370, -1308189874199616697817539200074238, 8289399765160712341131849367972542, -46783616321998478795458149057122145, 234999225964232933834149112694372867, -1049484407925242792828750467607365185, 4161052733141162438991333881629966449, -14620606470238507069638288669331531446, 45425825709704628283109430191976080400, -124468763777608175568796041188271717984, 299821137334135681782712542449338805040, -632525928565428301410709620694018226208, 1163532979856355964909411340878324232832, -1856399981685264274584742456532993660160, 2552803207326431764967213761527030470400, -3002667039899658352436610420272301120000, 2992862237498353265892271006627584000000, -2498577025975608447805248342475776000000, 1721249910903347055783181973286720000000, -959341910144268687109525373846400000000, 420984649108341364830441158592000000000, -139779856035015771303825062400000000000, 32957940077972879881652858880000000000, -4910962939069964235908198400000000000, 347259290825980971841536000000000000).

Crossrefs

Column k=8 of A154283.

Programs

Magma

[(&+[(-1)^j*Binomial(2*n+1, j)*Binomial(10-j, 2)^n: j in [0..8]]): n in [1..30]]; // G. C. Greubel, Sep 08 2022

Mathematica

With[{B=Binomial}, Table[Sum[(-1)^j*B[2n+1,j]*B[10-j,2]^n, {j,0,8}], {n, 30}]] (* G. C. Greubel, Sep 08 2022 *)

SageMath

def A151630(n): return sum((-1)^j*binomial(2*n+1, j)*binomial(10-j, 2)^n for j in (0..8))
[A151630(n) for n in (1..30)] # G. C. Greubel, Sep 08 2022

Formula

From G. C. Greubel, Sep 08 2022: (Start)

a(n) = Sum_{j=0..8} (-1)^j*binomial(2*n+1, j)*binomial(10-j, 2)^n.

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

Extensions

Terms a(11) and beyond from Andrew Howroyd, May 06 2020