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))))
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)))
A368587
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+4,5) / k!.
Original entry on oeis.org
0, 1, 4, 9, 20, 26, 96, -210, 2472, -20961, 211612, -2324729, 27901116, -362708320, 5077925048, -76168864092, 1218701840976, -20717931276243, 372922762998708, -7085532496941803, 141710649938878564, -2975923648716396714, 65470320271760793488
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))))
A368717
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^4 / k!.
Original entry on oeis.org
0, 1, 14, 39, 100, 125, 546, -1421, 15464, -132615, 1336150, -14683009, 176216844, -2290790411, 32071104170, -481066511925, 7697064256336, -130850092274191, 2355301661040414, -44750731559637545, 895014631192910900, -18795307255050934419
Offset: 0
-
f:= proc(n) option remember;
- n*procname(n-1)+n^4
end proc:
f(0):= 0:
seq(f(i),i=0..30); # Robert Israel, May 13 2025
-
Table[-n + 2*n^2 + n^3 + (-1)^n*n*Subfactorial[n-1], {n, 0, 20}] (* Vaclav Kotesovec, Jul 18 2025 *)
-
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, 4, stirling(4, k, 2)*x^k)*exp(x)/(1+x))))
Showing 1-4 of 4 results.