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 A062204 #26 Mar 23 2016 04:57:43
%S A062204 1,1,48639,75494983297,1177359342144641535,
%T A062204 103746115308050354021387521,36585008462723983824862891403150079,
%U A062204 41020870889694863957061607086939138327565057,124069835911824710311393852646151897334844371419287295
%N A062204 Number of alignments of n strings of length 7.
%C A062204 Strings of length 7 represent the average word length for most natural languages such as English. This sequence represents the search space for alignment and sequencing algorithms that work on multiple sets of strings.
%C A062204 The assertion that "strings of length 7 represent the average word length for most natural languages such as English" seems to conflict with studies that show that the average word length in English is about 4.5 letters and the average word length in modern Russian is 5.28 letters. - _M. F. Hasler_, Mar 12 2009
%C A062204 In general, row r > 0 of A262809 is asymptotic to sqrt(r*Pi) * (r^(r-1)/(r-1)!)^n * n^(r*n+1/2) / (2^(r/2) * exp(r*n) * (log(2))^(r*n+1)). - _Vaclav Kotesovec_, Mar 23 2016
%D A062204 M. S. Waterman, Introduction to Computational Biology: Maps, Sequences and Genomes, 1995.
%H A062204 Alois P. Heinz, <a href="/A062204/b062204.txt">Table of n, a(n) for n = 0..50</a>
%H A062204 M. A. Covington, <a href="http://www.covingtoninnovations.com/mc/number.pdf">The number of distinct alignments of two strings</a>, Journal of Quantitative Linguistics, Volume 11, no. 3 (2004), 173-182.
%H A062204 Michael S. Waterman, <a href="http://dornsife.usc.edu/labs/msw/">Home Page</a> (contains copies of his papers)
%F A062204 A(n, y) = sum(k=0,n*y, sum(t=0,k, (-1)^t * binomial(k,t) * binomial(k-t,y)^n )).
%F A062204 a(n) ~ sqrt(7*Pi) * (7^6/6!)^n * n^(7*n+1/2) / (2^(7/2) * exp(7*n) * (log(2))^(7*n+1)). - _Vaclav Kotesovec_, Mar 23 2016
%e A062204 A(2, 7) = 48639 since this represents the number of distinct alignments of 2 strings of length 7. All values in A(2,X) can be cross-validated against the Delannoy sequence D(X,X) A001850.
%t A062204 With[{r = 7}, Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, r]^k, {i, 0, j}], {j, 0, k*r}], {k, 1, 10}]}]] (* _Vaclav Kotesovec_, Mar 22 2016 *)
%Y A062204 Cf. A062205, A062208, A001850. A(2, X) represents Waterman's f function.
%Y A062204 Row n=7 of A262809.
%K A062204 nonn
%O A062204 0,3
%A A062204 _Angelo Dalli_, Jun 13 2001
%E A062204 Formula and sequence revised by _Max Alekseyev_, Mar 12 2009