3,1

The array A(k,n) = Product of first n k-gonal pyramidal numbers begins:

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..|n=1|n=2|..n=3|...n=4..|......n=5....|......n=6......|......n=7......|.......n=8.........|

k=3|.1.|.4.|..40.|....800.|.......28000.|.......1568000.|.....131712000.|.......15805440000.|A087047

k=4|.1.|.5.|..70.|...2100.|......115500.|......10510500.|....1471470000.|......300179880000.|

k=5|.1.|.6.|.108.|...4320.|......324000.|......40824000.|....8001504000.|.....2304433152000.|

k=6|.1.|.7.|.154.|...7700.|......731500.|.....117771500.|...29678418000.|....11040371496000.|

k=7|.1.|.8.|.208.|..12480.|.....1435200.|.....281299200.|...86640153600.|....39507910041600.|

k=8|.1.|.9.|.270.|.718900.|.....2551500.|.....589396500.|..214540326000.|...115851776040000.|

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Eric W. Weisstein, Pyramidal Number

A(k,n) = PRODUCT[j=1..n] (1/6)*j*(j+1)*[(k-2)*j+(5-k)].

a(3) = product of the first 3 triangular pyramidal (tetrahedral) numbers (A000292) = A087047(3) = 1 * 4 * 10 = 40.

a(4) = product of the first 4 square pyramidal numbers (A000330) = 1 * 5 * 14 * 30 = 2100.

a(5) = product of the first 5 pentagonal pyramidal numbers (A002411) = 1 * 6 * 18 * 40 * 75 = 324000.

a(6) = product of the first 6 hexagonal pyramidal numbers (A002412) = 1 * 7 * 22 * 50 * 95 * 161 = 117771500.

a(7) = product of the first 7 heptagonal pyramidal numbers (A002413) = 1 * 8 * 26 * 60 * 115 * 196 * 308 = 86640153600.

a(8) = product of the first 8 octagonal pyramidal numbers (A002414) = 1 * 9 * 30 * 70 * 135 * 231 * 364 * 540 = 115851776040000.

A130729 := proc(n) n!*(n+1)!*(n-2)^n*pochhammer(1+(5-n)/(n-2), n)/6^n ; end: seq(A130729(n), n=3..30) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2008

Cf. A000292, A000330, A002411, A002412, A002413, A002414, A140729.

Sequence in context: A147520 A143314 A060056 this_sequence A003741 A049215 A059948

Adjacent sequences: A140726 A140727 A140728 this_sequence A140730 A140731 A140732

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), May 25 2008

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2008