A323543
a(n) = Product_{k=0..n} (k^5 + (n-k)^5).
Original entry on oeis.org
0, 1, 2048, 64304361, 3995393327104, 775913238525390625, 320224500476333990608896, 273342392644434762426370643281, 429621172463958849019228299940855808, 1175198860360296464427314161342724729270241, 5278148679274118560000000000000000000000000000000
Offset: 0
Cf. 2*
A000539 (with sum instead of product).
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[(&*[(k^5 + (n-k)^5): k in [0..n]]): n in [0..12]]; // Vincenzo Librandi, Jan 18 2019
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Table[Product[k^5+(n-k)^5, {k, 0, n}], {n, 0, 12}]
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m=5; vector(12, n, n--; prod(k=0,n, k^m +(n-k)^m)) \\ G. C. Greubel, Jan 18 2019
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m=5; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..12)] # G. C. Greubel, Jan 18 2019
A323534
a(n) = Product_{k=1..n} (binomial(k-1,6) + binomial(n-k,6)).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2551486386077798400, 4356795681519916813516800, 8378295212644383454317143654400, 17729411415388061815791372479702630400, 47314452412112353657024080317791118400000000, 160496342476959706163534573940481304027441961369600
Offset: 0
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f:= proc(n) local k; mul(binomial(k-1,6)+binomial(n-k,6),k=1..n) end proc:
map(f, [$0..20]); # Robert Israel, Feb 01 2019
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Table[Product[Binomial[k-1,6] + Binomial[n-k,6], {k, 1, n}], {n, 0, 20}]
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a(n) = prod(k=1, n, binomial(k-1, 6) + binomial(n-k, 6)); \\ Daniel Suteu, Jan 17 2019
A323496
a(n) = Product_{k=1..n} (binomial(k-1,3) + binomial(n-k,3)).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 1600, 1280000, 1225000000, 1487467520000, 2342962705305600, 4757234928058368000, 12302981968140864000000, 39976163552160000000000000, 161025498138224463853824000000, 794000312545927932130993635328000, 4737527580526919896601692054005760000
Offset: 0
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Table[Product[Binomial[k-1,3] + Binomial[n-k,3], {k, 1, n}], {n, 0, 20}]
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a(n) = prod(k=1, n, binomial(k-1,3) + binomial(n-k,3)); \\ Michel Marcus, Jan 17 2019
A323497
a(n) = Product_{k=1..n} (binomial(k-1,4) + binomial(n-k,4)).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 6890625, 67528125000, 771895089000000, 10758502218240000000, 193672800442598400000000, 4520389860871215408000000000, 136445409183108034775390625000000, 5281556250358583667176941845984375000, 259600586924352252185403119405592275390625
Offset: 0
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Table[Product[Binomial[k-1,4] + Binomial[n-k,4], {k, 1, n}], {n, 0, 20}]
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a(n) = prod(k=1, n, binomial(k-1,4) + binomial(n-k,4)); \\ Michel Marcus, Jan 17 2019
A323535
a(n) = Product_{k=1..n} (binomial(k-1,7) + binomial(n-k,7)).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240248274716697412239360000, 5659588189073370681080838881280000, 148305406398618918682372310424354816000000, 4049882681498254991937037064898924144230400000000, 137651993399006086593846978063252515678682995490816000000
Offset: 0
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Table[Product[Binomial[k-1,7] + Binomial[n-k,7], {k, 1, n}], {n, 0, 20}]
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a(n) = prod(k=1, n, binomial(k-1, 7) + binomial(n-k, 7)); \\ Daniel Suteu, Jan 17 2019
A323538
a(n) = Product_{k=1..n} (binomial(k-1,8) + binomial(n-k,8)).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 676788847291127500630565286687890625, 224202413239751513418389758669186941328125000, 81789054189516490351294844356948943677175390625000000, 29455964980491136378751203264203423123185624125549245000000000
Offset: 0
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Table[Product[Binomial[k-1,8] + Binomial[n-k,8], {k, 1, n}], {n, 0, 20}]
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a(n) = prod(k=1, n, binomial(k-1, 8)+binomial(n-k, 8)) \\ Felix Fröhlich, Jan 17 2019
Showing 1-6 of 6 results.