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))))
A368767
a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * binomial(k+2,3) / k!).
Original entry on oeis.org
1, 0, 4, 2, 28, 105, 686, 4718, 37864, 340611, 3406330, 37469344, 449632492, 5845221941, 81833107734, 1227496615330, 19639945846096, 333879079382663, 6009823428889074, 114186645148891076, 2283732902977823060, 47958390962534282489, 1055084601175754216782
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)))
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))))
A368716
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^3 / k!.
Original entry on oeis.org
0, 1, 6, 9, 28, -15, 306, -1799, 14904, -133407, 1335070, -14684439, 176214996, -2290792751, 32071101258, -481066515495, 7697064252016, -130850092279359, 2355301661034294, -44750731559644727, 895014631192902540, -18795307255050944079
Offset: 0
-
f:= proc(n) option remember;
- n*procname(n-1)+n^3
end proc:
f(0):= 0:
seq(f(i),i=0..30); # Robert Israel, May 13 2025
-
Table[n + n^2 + (-1)^n*n*Subfactorial[n-1], {n, 0, 20}] (* Vaclav Kotesovec, Jul 18 2025 *)
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my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, 3, stirling(3, k, 2)*x^k)*exp(x)/(1+x))))
Showing 1-4 of 4 results.
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