Original entry on oeis.org
1, 1, 3, 43, 5949, 12950796, 586826390263, 669793946192984257, 22558227235537152753501561, 25741074696455818592335996518315259, 1124843928218943684789052411802502269971863691, 2100464404490451025972467064515428575200326254804659324780
Offset: 0
-
b:= proc(n, k) option remember; `if`(n=0, 1,
add(k^j*binomial(n-1, j)*b(j, k), j=0..n-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..12); # Alois P. Heinz, Jul 28 2019
-
b[0, _] = 1;
b[n_, k_] := b[n, k] = Sum[k^j Binomial[n-1, j] b[j, k], {j, 0, n-1}];
a[n_] := b[n, n];
a /@ Range[0, 12] (* Jean-François Alcover, Nov 14 2020, after Alois P. Heinz *)
-
def ncr(n, r)
return 1 if r == 0
(n - r + 1..n).inject(:*) / (1..r).inject(:*)
end
def A(k, n)
ary = [1]
(1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + k ** j * ncr(i - 1, j) * ary[j]}}
ary
end
def A309401(n)
(0..n).map{|i| A(i, i)}
end
p A309401(20)
A126443
a(n) = Sum_{k=0..n-1} C(n-1,k)*a(k)*2^k for n>0, with a(0)=1.
Original entry on oeis.org
1, 1, 3, 17, 179, 3489, 127459, 8873137, 1195313043, 315321098561, 164239990789571, 169810102632595281, 349630019758589841523, 1436268949679165936016097, 11784559509424676876673518499, 193243076262167105764611875139569
Offset: 0
-
a(n)=if(n==0,1,sum(k=0,n-1,binomial(n-1,k)*a(k)*2^k))
A355081
G.f. A(x) satisfies A(x) = 1 + x * A(3 * x / (1 - x)) / (1 - x).
Original entry on oeis.org
1, 1, 4, 43, 1279, 108472, 26888677, 19761575473, 43356335678176, 284807217244068223, 5608422162798704960959, 331227791701602557410058404, 58679652813856265804094312228601, 31185477505022553490008128886444268657
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, 3^j*binomial(i-1, j)*v[j+1])); v;
A355082
G.f. A(x) satisfies A(x) = 1 + x * A(4 * x / (1 - x)) / (1 - x).
Original entry on oeis.org
1, 1, 5, 89, 5949, 1546225, 1591006901, 6526287232201, 106972340665773165, 7011394913950382306529, 1838058207026378316690626149, 1927362102757461997768349891040825, 8083963777926072174628168609626454270621
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, 4^j*binomial(i-1, j)*v[j+1])); v;
Showing 1-4 of 4 results.
Comments