A062205
Number of alignments of n strings of length 4.
Original entry on oeis.org
1, 1, 321, 699121, 5552351121, 117029959485121, 5402040231378569121, 480086443888959812703121, 74896283763383392805211587121, 19133358944433370977791260580721121, 7581761490297442738124283591348762605121, 4461925444770180839552702516305804230194739121
Offset: 0
See
A062204 for references, formulas and comments.
-
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 *)
Original entry on oeis.org
1, 1, 9, 169, 5625, 292681, 21930489, 2236627849, 297935847225, 50229268482121, 10454564139438969, 2632936466960600329, 789136169944454084025, 277579719258755165321161, 113238180214596650771616249, 53030348046942317338336489609, 28256184698070300360908567636025
Offset: 0
-
b:= proc(n, k) option remember;
`if`(n=0, 1, add(b(n-1, j)*j, j=k..k+1))
end:
a:= n-> b(n, 0)^2:
seq(a(n), n=0..16); # Alois P. Heinz, Aug 12 2025
-
Table[(PolyLog[ -z, 1/2]/2)^2, {z, 1, 16}] (* Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006 *)
-
{a(n)=sum(k=0, n, stirling(n, k, 2)*k!)^2} \\ Paul D. Hanna, Nov 07 2009
More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006
A384351
Expansion of Product_{k>=1} 1/(1 - k*(k+1)/2 * x)^((1/2)^(k+2)).
Original entry on oeis.org
1, 1, 7, 143, 6140, 455828, 51947988, 8414718996, 1836791273514, 519582028795210, 184852108308617398, 80776494267416227078, 42529172631705836804876, 26553065315757661351020284, 19397441882229095276127402500, 16390942374821715002096327774628
Offset: 0
-
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[Sum[(-1)^j*Binomial[i, j]*((i - j)*(i - j - 1)/2)^k, {j, 0, i}], {i, 0, 2 k}]*x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 29 2025 *)
-
a262809(n, k) = sum(i=0, k*n, sum(j=0, i, (-1)^j*binomial(i, j)*binomial(i-j, n)^k));
my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a262809(2, k)*x^k/k)))
Comments