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 A191899 #19 Jul 22 2025 12:11:34
%S A191899 0,128,3280,32768,195312,839808,2882400,8388608,21523360,50000000,
%T A191899 107179440,214990848,407865360,737894528,1281445312,2147483648,
%U A191899 3487878720,5509980288,8491781520,12800000000,18911429680,27437936768,39155492640,55037657088,76293945312,104413532288
%N A191899 Number of compositions of odd natural numbers into 8 parts <=n.
%H A191899 Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>
%H A191899 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (8,-27,48,-42,0,42,-48,27,-8,1).
%F A191899 a(n) = 1/2*((n + 1)^8 - (1 + (-1)^n)/2).
%F A191899 G.f.: -16*x*(8*x^6+141*x^5+624*x^4+974*x^3+624*x^2+141*x+8) / ((x-1)^9*(x+1)). - _Colin Barker_, May 16 2013
%e A191899 a(1)=128 compositions of odd numbers into 8 parts <=1
%e A191899 1:(0,0,0,0,0,0,0,1)-->8!/(7!1!)= 8
%e A191899 3:(0,0,0,0,0,1,1,1)-->8!/(5!3!)=56
%e A191899 5:(0,0,0,1,1,1,1,1)-->8!/(3!5!)=56
%e A191899 7:(0,1,1,1,1,1,1,1)-->8!/(1!7!)= 8
%e A191899 -------------------------------------
%e A191899 128
%t A191899 Table[Floor[1/2*((n + 1)^8 - (1 + (-1)^n)/2)], {n, 0, 25}]
%t A191899 LinearRecurrence[{8,-27,48,-42,0,42,-48,27,-8,1},{0,128,3280,32768,195312,839808,2882400,8388608,21523360,50000000},30] (* _Harvey P. Dale_, Aug 30 2016 *)
%o A191899 (PARI) a(n)=1/2*((n+1)^8-(1+(-1)^n)/2) \\ _Charles R Greathouse IV_, Jul 06 2017
%K A191899 nonn,easy
%O A191899 0,2
%A A191899 _Adi Dani_, Jun 19 2011