A374878
Obverse convolution (3n+2)**(3n+2); see Comments.
Original entry on oeis.org
4, 49, 1000, 28561, 1048576, 47045881, 2494357888, 152587890625, 10578455953408, 819628286980801, 70188843638032384, 6582952005840035281, 671088640000000000000, 73885357344138503765449, 8737103395697172336050176, 1104427674243920646305299201
Offset: 0
-
s[n_] := 3 n + 2; t[n_] := 3 n + 2;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 17}]
(* or *)
Table[(3*n+4)^(n+1), {n,0,20}] (* Vaclav Kotesovec, Sep 13 2024 *)
A374886
Obverse convolution (n^2)**(n^3); see Comments.
Original entry on oeis.org
0, 1, 64, 10935, 3440640, 1819796875, 1496658788352, 1803211314966369, 3041248222904320000, 6927551870579340989625, 20704007211909120000000000, 79269804046766547371821983319, 381109146011936063547707158953984, 2261992022793941981178428306342521875
Offset: 0
-
s[n_] := n^2; t[n_] := n^3;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]
A375050
Obverse convolution (n(n+1)/2)**(n(n+1)/2); see Comments.
Original entry on oeis.org
0, 1, 18, 576, 29400, 2205225, 228953088, 31473598464, 5537223659520, 1213834310015625, 324468643299372000, 103900389446258786304, 39267840204934404964992, 17296280109081832136303025, 8783270052027947513856000000, 5094007565002120817604034560000
Offset: 0
-
t:= n-> n*(n+1)/2:
a:= n-> mul(t(n-j)+t(j), j=0..n):
seq(a(n), n=0..15); # Alois P. Heinz, Aug 02 2024
-
s[n_] := n (n + 1)/2;
u[n_] := Product[s[k] + s[n - k], {k, 0, n}];
Table[u[n], {n, 0, 20}]
A375051
Obverse convolution (n^2 - 1)**(n^2 - 1); see Comments.
Original entry on oeis.org
-2, 1, 0, 441, 75264, 14402025, 3451797504, 1043554187025, 392874877255680, 181193143212358641, 100757479882752000000, 66592039534109652160521, 51648427918242896412672000, 46486269540273907302519872025, 48078115878910207012782666153984
Offset: 0
-
s[n_] := n^2 - 1; t[n_] := n^2 - 1;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}];
Table[u[n], {n, 0, 20}]
A375058
(1/4)*(obverse convolution (n^2 + n)**(n^2 + n)); see Comments.
Original entry on oeis.org
0, 1, 36, 2304, 235200, 35283600, 7326498816, 2014310301696, 708764628418560, 310741583364000000, 166127945369278464000, 106393998792968997175296, 80420536739705661368303616, 70845563326799184430297190400, 71952548266212946033508352000000
Offset: 0
-
s[n_] := n^2 + n; t[n_] := n^2 + n;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}];
Table[u[n]/4, {n, 0, 20}]
Original entry on oeis.org
4, 9, 50, 576, 12150, 529984, 46080000, 8227578436, 3001814235000, 2250930099585024, 3467943896484375000, 10990843331383915704576, 71660705425234329600000000, 961449528856034873335986864784, 26545636210087637565464331562500000
Offset: 0
-
s[n_] := LucasL[n]; t[n_] := LucasL[n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]
Original entry on oeis.org
4, 25, 294, 5184, 169000, 6350400, 331218944, 18517766400, 1288408000000, 124147372916736, 12047030383804416, 1481741383824000000, 199987846858565222400, 26836516406718627840000, 3937581724026934119628800, 668393794316928024576000000, 130212266115912538521600000000, 25085181032622344612780605440000
Offset: 1
-
s[n_] := Prime[n]; t[n_] := Prime[n];
u[n_] := Product[s[k] + t[n + 1 - k], {k, 1, n}]
Table[u[n], {n, 1, 18}]
A374852
a(n) = (1/3)*A054640(n) for n >= 1.
Original entry on oeis.org
1, 4, 24, 192, 2304, 32256, 580608, 11612160, 278691840, 8360755200, 267544166400, 10166678323200, 427000489574400, 18788021541273600, 901825033981132800, 48698551834981171200, 2921913110098870272000, 181158612826129956864000, 12318785672176837066752000
Offset: 1
-
s[n_] := 1; t[n_] := Prime[n];
u[n_] := Product[s[k] + t[n + 1 - k], {k, 1, n}]
(1/3) Table[u[n], {n, 1, 25}]
A374853
Obverse convolution (n)**(Prime(n)); see Comments.
Original entry on oeis.org
3, 16, 150, 2016, 42336, 1048320, 33679800, 1203840000, 51753461760, 2778808032000, 158404546460160, 10690579965542400, 793627573939200000, 61438811607613440000, 5171227710555658752000, 488050626303556459315200, 50980860352307128320000000
Offset: 1
-
s[n_] := n; t[n_] := Prime[n];
u[n_] := Product[s[k] + t[n + 1 - k], {k, 1, n}]
Table[u[n], {n, 1, 20}]
A374857
Obverse convolution (n)**(Fibonacci(n)); see Comments.
Original entry on oeis.org
0, 1, 4, 36, 432, 8000, 216000, 8668296, 516311040, 46066268160, 6197083200000, 1266665976576000, 396044443339776000, 190620194701725734400, 142017680690039344619520, 164583068009095149120000000, 297947499870194922871259136000
Offset: 0
-
s[n_] := n; t[n_] := Fibonacci[n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]
Comments