A368574
a(n) = n! * Sum_{k=0..n} binomial(k+2,3) / k!.
Original entry on oeis.org
0, 1, 6, 28, 132, 695, 4226, 29666, 237448, 2137197, 21372190, 235094376, 2821132876, 36674727843, 513446190362, 7701692856110, 123227085698576, 2094860456876761, 37707488223782838, 716442276251875252, 14328845525037506580, 300905756025787639951, 6619926632567328080946
Offset: 0
-
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 2, binomial(2, k)*x^k/(k+1)!)*exp(x)/(1-x))))
A368586
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+3,4) / k!.
Original entry on oeis.org
0, 1, 3, 6, 11, 15, 36, -42, 666, -5499, 55705, -611754, 7342413, -95449549, 1336296066, -20044437930, 320711010756, -5452087178007, 98137569210111, -1864613814984794, 37292276299704735, -783137802293788809, 17229031650463366448, -396267727960657413354
Offset: 0
-
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 3, binomial(3, k)*x^k/(k+1)!)*exp(x)/(1+x))))
A368576
a(n) = n! * Sum_{k=0..n} binomial(k+4,5) / k!.
Original entry on oeis.org
0, 1, 8, 45, 236, 1306, 8088, 57078, 457416, 4118031, 41182312, 453008435, 5436105588, 70669378832, 989371312216, 14840569694868, 237449115133392, 4036634957288013, 72659429231210568, 1380529155393034441, 27610583107860731324, 579822245265075410934
Offset: 0
-
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 4, binomial(4, k)*x^k/(k+1)!)*exp(x)/(1-x))))
A368764
a(n) = n! * (1 + Sum_{k=0..n} binomial(k+3,4) / k!).
Original entry on oeis.org
1, 2, 9, 42, 203, 1085, 6636, 46662, 373626, 3363129, 33632005, 369953056, 4439438037, 57712696301, 807977750594, 12119666261970, 193914660195396, 3296549223326577, 59337886019884371, 1127419834377810364, 22548396687556216135, 473516330438680549461
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)))
Showing 1-4 of 4 results.