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 A062205 Number of alignments of n strings of length 4. 4
 1, 1, 321, 699121, 5552351121, 117029959485121, 5402040231378569121, 480086443888959812703121, 74896283763383392805211587121, 19133358944433370977791260580721121, 7581761490297442738124283591348762605121, 4461925444770180839552702516305804230194739121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjectures: a(n) == 1 (mod 80); for fixed k, the sequence a(n) (mod k) eventually becomes periodic. - Peter Bala, Dec 19 2019 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 FORMULA From Vaclav Kotesovec, Mar 22 2016: (Start) a(n) ~ 2^(5*n-3) * n!^4 / (Pi^(3/2) * n^(3/2) * 3^n * (log(2))^(4*n+1)). a(n) ~ sqrt(Pi) * 2^(5*n-1) * n^(4*n+1/2) / (3^n * exp(4*n) * (log(2))^(4*n+1)). (End) It appears that a(n) = (1/(2*6^n))*Sum_{k = 0..n} (-1)^(n-k)*binomial(n,k) *A055203(n+k) for n >= 1. - Peter Bala, Dec 19 2019 MATHEMATICA With[{r = 4}, Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, r]^k, {i, 0, j}], {j, 0, k*r}], {k, 1, 15}]}]] (* Vaclav Kotesovec, Mar 22 2016 *) CROSSREFS See A062204 for references, formulas and comments. Row n=4 of A262809. Sequence in context: A144124 A090101 A105952 * A054034 A004947 A004967 Adjacent sequences:  A062202 A062203 A062204 * A062206 A062207 A062208 KEYWORD nonn AUTHOR Angelo Dalli, Jun 13 2001 EXTENSIONS Revised by Max Alekseyev, Mar 13 2009 STATUS approved

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Last modified May 17 06:30 EDT 2021. Contains 343965 sequences. (Running on oeis4.)