A151631 Number of permutations of 2 indistinguishable copies of 1..n with exactly 9 adjacent element pairs in decreasing order.

0, 0, 0, 0, 0, 716, 6030140, 6727188848, 2898916824320, 713977455470200, 121976270685699352, 16151017610840330800, 1776999565259831468176, 170177528415687895764196, 14652450038892876986833140, 1161079239300986084649361440, 86154881092488160155801056400

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 (715, -246246, 54441244, -8688122872, 1067021500896, -104995425911880, 8509695500071416, -579576260744202564, 33677542872235956572, -1689382985951061375584, 73851002736478171785480, -2834880964029477987484784, 96157307046055530022659296, -2897042624210196682636584168, 77864265942445209589091609880, -1873766333805076180258298532750, 40496615572103854298268667369290, -788076483208734925614168894880060, 13838951374046160498670120531900480, -219687004175759538500502785436424080, 3157288221085995379662504956708878000, -41129275275200013601737955696226964280, 486094673693240626024143992242097156520, -5215868577535025043910503669088440816660, 50836490264499322636673534370758109300396, -450178157479731675331980353762821217397840, 3622293207037319736887764557341829467018616, -26480103842294874673252984165092468826819824, 175815364714697377375288287523495537964680512, -1059685472384814743761882978983528331243780536, 5794006095745855069703806488744115029544310280, -28712845744794238874234856225294257655712864281, 128823074763417157330327450612996297705760524899, -522591702536253659265150517358362904804073702702, 1913877482958449061349927143878484707275902379044, -6316428749606413461495948122861485717837380579480, 18747314973123796053526567679937869016617533512144, -49921577593788411541183731318082844750585106215136, 118943703030207917584554870579506771381266070945088, -252783808588069216519093758900774170980091669600640, 477488323849250418683533669723998946360819532025600, -798356115352276242760013175029559061134250770240000, 1175928120255423597428632028457343135596494440320000, -1517382017920428119910882859627104065334963129600000, 1704039910436999395713170098091040014017105344000000, -1652387285823260958429823161445909045075804800000000, 1370326851226558633202522928960523884556128000000000, -960372144298001827617428397061627444681920000000000, 560220235705759309094565929790235607973120000000000, -266618977212745148402028435378503712537600000000000, 100714095994301538183255879386079220224000000000000, -29009478229516455744577541121897523200000000000000, 5977866876033168754616374301599948800000000000000, -783993082018895079509762803666944000000000000000, 49121618545275670528799969525760000000000000000).

Crossrefs

Column k=9 of A154283.

Programs

Magma

[(&+[(-1)^j*Binomial(2*n+1, j)*Binomial(11-j, 2)^n: j in [0..9]]): n in [1..30]]; // G. C. Greubel, Sep 08 2022

Mathematica

With[{B=Binomial}, Table[Sum[(-1)^j*B[2n+1, j]*B[11-j, 2]^n, {j,0,9}], {n, 30}]] (* G. C. Greubel, Sep 08 2022 *)

SageMath

def A151631(n): return sum((-1)^j*binomial(2*n+1, j)*binomial(11-j, 2)^n for j in (0..9))
[A151631(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..9} (-1)^j*binomial(2*n+1, j)*binomial(11-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