A151646 Number of permutations of 4 indistinguishable copies of 1..n with exactly 8 adjacent element pairs in decreasing order.

0, 0, 1, 4961755, 93200908410, 342907451401150, 580563155365559991, 636819836268006188325, 536414785137072299859000, 381545916738691833553696960, 242640958318176281706165559005, 143034343946525950106468425526767, 80029528286823033581035280235294534

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 (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).

Crossrefs

Column k=8 of A236463.

Programs

Magma

[(&+[(-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

Mathematica

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 *)

SageMath

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

Formula

From G. C. Greubel, Sep 12 2022: (Start)

a(n) = Sum_{j=0..8} (-1)^j*binomial(4*n+1, j)*binomial(12-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