A151645 Number of permutations of 4 indistinguishable copies of 1..n with exactly 7 adjacent element pairs in decreasing order.

0, 0, 112, 15018688, 69830127680, 99825129369600, 79985306860607376, 46314409921814756480, 22045769335091544766944, 9274231983519733250418880, 3600979296578512256763795120, 1326029824370661243342378614592, 471290654822091236131899199410048

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 (1716, -1336335, 629496840, -201662851530, 46822832504112, -8198705689543922, 1112168992680480840, -119141036496502877115, 10222470418101608725380, -710028695676774672446661, 40247505166008930895508256, -1873377747222689750364984480, 71937847093856988824912606400, -2286774193421516436467863123500, 60320306153033851397466880890000, -1322308197142100207034150164034375, 24106927359036759704772726680437500, -365500263926394882030626778788515625, 4605433354261294678893837507628125000, -48161866919161309147628101483394531250, 417169217807133892391665295808281250000, -2984883489620059230375322457959863281250, 17581782760938948426247013769884765625000, -84895915778539297273671354596768798828125, 334334731338183313104706151801440429687500, -1067327299326747481004612649706512451171875, 2742187962577531073301464459260253906250000, -5621703251054691311256555851797485351562500, 9102454366374887952005021014892578125000000, -11493168657532067651650712133178710937500000, 11128534281634369331848951098632812500000000, -8070567814684173335537005554199218750000000, 4229549688642245394265986328125000000000000, -1509576063065432132950057983398437500000000, 327876672867164207503417968750000000000000, -32668871390750056907043457031250000000000).

Crossrefs

Column k=7 of A236463.

Programs

Magma

[(&+[(-1)^j*Binomial(4*n+1, j)*Binomial(11-j, 4)^n: j in [0..7]]): n in [1..30]]; // G. C. Greubel, Sep 12 2022

Mathematica

Table[Sum[(-1)^j*Binomial[4*n+1, j]*Binomial[11-j, 4]^n, {j,0,7}], {n, 30}] (* G. C. Greubel, Sep 12 2022 *)

SageMath

def A151645(n): return sum((-1)^j*binomial(4*n+1, j)*binomial(11-j, 4)^n for j in (0..7))
[A151645(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..7} (-1)^j*binomial(4*n+1, j)*binomial(11-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