A368575
a(n) = n! * Sum_{k=0..n} binomial(k+3,4) / k!.
Original entry on oeis.org
0, 1, 7, 36, 179, 965, 5916, 41622, 333306, 3000249, 30003205, 330036256, 3960436437, 51485675501, 720799459394, 10811991893970, 172991870307396, 2940861795230577, 52935512314156371, 1005774733968978364, 20115494679379576135, 422425388266971109461
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))))
A368585
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+2,3) / k!.
Original entry on oeis.org
0, 1, 2, 4, 4, 15, -34, 322, -2456, 22269, -222470, 2447456, -29369108, 381798859, -5345183466, 80177752670, -1282844041904, 21808348713337, -392550276838926, 7458455259940924, -149169105198816940, 3132551209175157511, -68916126601853463218
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))))
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))))
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 1-4 of 4 results.