A151645
Number of permutations of 4 indistinguishable copies of 1..n with exactly 7 adjacent element pairs in decreasing order.
Original entry on oeis.org
0, 0, 112, 15018688, 69830127680, 99825129369600, 79985306860607376, 46314409921814756480, 22045769335091544766944, 9274231983519733250418880, 3600979296578512256763795120, 1326029824370661243342378614592, 471290654822091236131899199410048
Offset: 1
- 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).
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[(&+[(-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
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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 *)
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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
A151646
Number of permutations of 4 indistinguishable copies of 1..n with exactly 8 adjacent element pairs in decreasing order.
Original entry on oeis.org
0, 0, 1, 4961755, 93200908410, 342907451401150, 580563155365559991, 636819836268006188325, 536414785137072299859000, 381545916738691833553696960, 242640958318176281706165559005, 143034343946525950106468425526767, 80029528286823033581035280235294534
Offset: 1
- 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 (3003, -4162873, 3551061531, -2096207060005, 912895579221687, -305328609273397721, 80608589410303191531, -17133574981653166325177, 2975751362327641235971395, -427142014842027656374910861, 51127014764298024327411188343, -5139329342457472614658424097033, 436312819970914193848847127900771, -31426243951346569405904042968530765, 1927342211018620664279773806724715175, -100933285880815016603295952121830038375, 4523504144544821353415456937942775288125, -173776985561841775826234927570092358346875, 5729043172063166741006217399985894359890625, -162198131836401649898699895818566956753359375, 3944628225019940257125376396708675533889453125, -82398217846689093833779870805804283233029296875, 1477665338729728226836090671986711982376025390625, -22731084147456462550530779048053669604524169921875, 299595222223163468987754350912060965900683837890625, -3377919623847932084067870292992011095430023193359375, 32518626462136659325409491517944655940664581298828125, -266676183001740854147840292513976704896348114013671875, 1857917085133334670906077230143918647920346832275390625, -10961838772225480653519248240736047402182399749755859375, 54571211801311516391138462683664922968171710968017578125, -228261653468654128204347312823339756274744796752929687500, 798336270099879773176526522355047534756042861938476562500, -2321717655620409519686803878550886844161888122558593750000, 5578739689255747247427306410125699228817481994628906250000, -10994370061596358240933839300508579740941619873046875000000, 17618151169077562279562894597453637768482208251953125000000, -22717852210784784346861189272915561466140747070312500000000, 23262654950653352840100935376081129626083374023437500000000, -18587207297353255408930961526285245155334472656250000000000, 11305873010139687266158804088554830436706542968750000000000, -5044520716275709824570004495558783721923828125000000000000, 1553839409218924943369495099604320526123046875000000000000, -294840938867578931210874908494949340820312500000000000000, 25946002620346945946556991947555541992187500000000000000).
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[(&+[(-1)^j*Binomial(4*n+1, j)*Binomial(12-j, 4)^n: j in [0..8]]): n in [1..30]]; // G. C. Greubel, Sep 12 2022
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Table[Sum[(-1)^j*Binomial[4*n+1, j]*Binomial[12-j, 4]^n, {j,0,8}], {n, 30}] (* G. C. Greubel, Sep 12 2022 *)
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def A151646(n): return sum((-1)^j*binomial(4*n+1, j)*binomial(12-j, 4)^n for j in (0..8))
[A151646(n) for n in (1..30)] # G. C. Greubel, Sep 12 2022