A371341
G.f. A(x) satisfies A(x) = 1 + x/A(x) * (1 + A(x)^5).
Original entry on oeis.org
1, 2, 6, 46, 330, 2778, 24094, 219318, 2048274, 19583410, 190497142, 1880184446, 18778814938, 189456108554, 1927852050830, 19763367194630, 203919590002210, 2116079501498722, 22069907395614182, 231222485352688590, 2432325883912444010
Offset: 0
-
A371341 := proc(n)
if n = 0 then
1;
else
add(binomial(n,k)*binomial(2*n-5*k-2,n-1),k=0..n) ;
(-1)^(n-1)*%/n ;
end if;
end proc:
seq(A371341(n),n=0..60) ; # R. J. Mathar, Apr 22 2024
-
a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(2*n-5*k-2, n-1))/n);
A349011
G.f. A(x) satisfies: A(x) = (1 - x * A(-x)) / (1 - 2 * x * A(x)).
Original entry on oeis.org
1, 1, 5, 17, 105, 433, 2925, 13185, 93425, 443009, 3233205, 15840209, 117950745, 591187953, 4466545245, 22766535297, 173906505825, 897941153665, 6918379345125, 36089242700049, 279988660639305, 1472715584804529, 11490841104036045, 60857608450349313, 477104721264920145
Offset: 0
-
A349011 := proc(n)
option remember ;
if n = 0 then
1;
else
(-1)^n*procname(n-1)+2*add(procname(k)*procname(n-k-1),k=0..n-1) ;
end if;
end proc:
seq(A349011(n),n=0..40) ; # R. J. Mathar, Aug 19 2022
-
nmax = 24; A[] = 0; Do[A[x] = (1 - x A[-x])/(1 - 2 x A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = (-1)^n a[n - 1] + 2 Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]
A371892
G.f. A(x) satisfies A(x) = 1 + x/A(x) * (1 + A(x)^4).
Original entry on oeis.org
1, 2, 4, 24, 112, 688, 4032, 25856, 165888, 1103616, 7412480, 50699776, 350087168, 2444208128, 17198686208, 121945948160, 870026493952, 6242802761728, 45016506564608, 326071359897600, 2371312632397824, 17307835567636480, 126743329792327680
Offset: 0
-
a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(2*n-4*k-2, n-1))/n);
Showing 1-3 of 3 results.