A368768
a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * binomial(k+3,4) / k!).
Original entry on oeis.org
1, 0, 5, 0, 35, 105, 756, 5082, 40986, 368379, 3684505, 40528554, 486344013, 6322470349, 88514587266, 1327718805930, 21243500898756, 361139515274007, 6500511274938111, 123509714223816794, 2470194284476344735, 51874079974003228809, 1141229759428071046448
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*sum(k=0, 3, binomial(3, k)*(-x)^k/(k+1)!)*exp(-x))/(1-x)))
A368762
a(n) = n! * (1 + Sum_{k=0..n} binomial(k+1,2) / k!).
Original entry on oeis.org
1, 2, 7, 27, 118, 605, 3651, 25585, 204716, 1842489, 18424945, 202674461, 2432093610, 31617217021, 442641038399, 6639615576105, 106233849217816, 1805975436703025, 32507557860654621, 617643599352437989, 12352871987048759990, 259410311728023960021
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x*sum(k=0, 1, binomial(1, k)*x^k/(k+1)!)*exp(x))/(1-x)))
A368763
a(n) = n! * (1 + Sum_{k=0..n} binomial(k+2,3) / k!).
Original entry on oeis.org
1, 2, 8, 34, 156, 815, 4946, 34706, 277768, 2500077, 25000990, 275011176, 3300134476, 42901748643, 600624481562, 9009367224110, 144149875586576, 2450547884972761, 44109861929510838, 838087376660707252, 16761747533214146580, 351996698197497079951
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x*sum(k=0, 2, binomial(2, k)*x^k/(k+1)!)*exp(x))/(1-x)))
Showing 1-3 of 3 results.