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.
%I A383840 #23 May 12 2025 11:53:59
%S A383840 1,55,2002,61490,1733303,46587905,1217854704,31306548900,796513723005,
%T A383840 20135227330075,506945890951006,12730754139133030,319183135225967507,
%U A383840 7994212035818175365,200089485703376577308,5005984516439566690680,125209574645032904521209
%N A383840 Expansion of 1/((1-x) * (1-4*x) * (1-9*x) * (1-16*x) * (1-25*x)).
%H A383840 Seiichi Manyama, <a href="/A383840/b383840.txt">Table of n, a(n) for n = 0..714</a>
%H A383840 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (55,-1023,7645,-21076,14400).
%F A383840 a(n) = A269945(n+5,5).
%F A383840 a(n) = 55*a(n-1) - 1023*a(n-2) + 7645*a(n-3) - 21076*a(n-4) + 14400*a(n-5).
%F A383840 a(n) = (5*25^(n+4) - 2*16^(n+5) + 9^(n+6) - 6*4^(n+6) + 42)/362880.
%F A383840 sinh(x)^10/10! = Sum_{k>=0} 4^k * a(k) * x^(2*k+10)/(2*k+10)!.
%F A383840 a(n) = (1/10!) * Sum_{k=0..10} (-1)^k * (5-k)^(2*n+10) * binomial(10,k).
%F A383840 a(n) = Sum_{k=0..2*n} (-5)^k * binomial(2*n+10,k) * Stirling2(2*n-k+10,10).
%F A383840 a(n) = Sum_{k=0..2*n} (-1)^k * Stirling2(k+5,5) * Stirling2(2*n-k+5,5).
%o A383840 (PARI) a(n) = (5*25^(n+4)-2*16^(n+5)+9^(n+6)-6*4^(n+6)+42)/362880;
%Y A383840 Cf. A269945, A383838.
%K A383840 nonn,easy
%O A383840 0,2
%A A383840 _Seiichi Manyama_, May 11 2025