cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A336513 a(n) = Sum_{i=1..n} Product_{j=(i-1)*n+1..i*n} j.

This page as a plain text file.
%I A336513 #19 May 01 2021 17:41:14
%S A336513 1,14,630,57264,8626800,1940869440,609372212400,254507088084480,
%T A336513 136432540607489280,91303132805512992000,74605774050426543724800,
%U A336513 73097485140038735163110400,84588938888439008795675904000,114144070365165930162064530739200,177648727691418999798103189989120000
%N A336513 a(n) = Sum_{i=1..n} Product_{j=(i-1)*n+1..i*n} j.
%H A336513 Seiichi Manyama, <a href="/A336513/b336513.txt">Table of n, a(n) for n = 1..214</a>
%F A336513 a(n) = n! * A096131(n) = n! * Sum_{k=1..n} binomial(k*n, n).
%e A336513 a(2) = 1*2 + 3*4 = 14.
%e A336513 a(3) = 1*2*3 + 4*5*6 + 7*8*9 = 630.
%e A336513 a(4) = 1*2*3*4 + 5*6*7*8 + 9*10*11*12 + 13*14*15*16 = 57264.
%t A336513 a[n_] := n! * Sum[Binomial[k*n, n], {k, 1, n}]; Array[a, 15] (* _Amiram Eldar_, May 01 2021 *)
%o A336513 (PARI) {a(n) = sum(i=1, n, prod(j=(i-1)*n+1,i*n, j))}
%Y A336513 Main diagonal of A333446.
%Y A336513 Cf. A096131, A336502.
%K A336513 nonn,easy
%O A336513 1,2
%A A336513 _Seiichi Manyama_, Jul 23 2020