Original entry on oeis.org
1, 2, 10, 80, 838, 10952, 171910, 3148280, 65890198, 1551389192, 40586247910, 1167964662680, 36666464437558, 1247011549249832, 45672691012357510, 1792280373542404280, 75021202465129000918, 3336499249170658956872, 157116438405334017308710, 7809681380575733223237080, 408621675981135189773468278
Offset: 0
-
def a(n):
if n==0:
return 1
else:
return (-1)^n + sum([(1-(-2)^j)*binomial(n,j)*a(n-j) for j in [1,..,n]])
list(a(n) for n in [0,..,20])
-
f= e^(x)/(1 + e^(2*x) - e^(3*x))
print([(diff(f,x,i)).subs(x=0) for i in [0,..,20]])
A355408
Expansion of e.g.f. 1/(1 + exp(x) - exp(3*x)).
Original entry on oeis.org
1, 2, 16, 170, 2416, 42962, 916696, 22819610, 649207456, 20778364322, 738918769576, 28905116527850, 1233506128752496, 57025618592932082, 2839117599033828856, 151446758367400488890, 8617182795217834505536, 520954229292164353554242
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+exp(x)-exp(3*x))))
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (3^j-1)*binomial(i, j)*v[i-j+1])); v;
A355411
Expansion of e.g.f. 1/(3 - exp(2*x) - exp(3*x)).
Original entry on oeis.org
1, 5, 63, 1175, 29211, 907775, 33852603, 1472830175, 73232729451, 4096474833695, 254608472798043, 17407167078420575, 1298290575826434891, 104900562662494154015, 9127848307446874753083, 850985644429074730049375, 84626187772620135685119531
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(3-exp(2*x)-exp(3*x))))
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (3^j+2^j)*binomial(i, j)*v[i-j+1])); v;
A368015
Expansion of e.g.f. 1/(1 - exp(2*x) + exp(3*x)).
Original entry on oeis.org
1, -1, -3, 5, 81, 29, -4623, -20035, 415041, 4838909, -46093743, -1309934275, 3230184801, 419574363389, 2065056788337, -154120122603715, -2307971235744639, 59954627542249469, 1959892188447337617, -19474957767402204355, -1658215397958862557279
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (2^j-3^j)*binomial(i, j)*v[i-j+1])); v;
Showing 1-4 of 4 results.