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
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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)))
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
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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)))
A368765
a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * k / k!).
Original entry on oeis.org
1, 0, 2, 3, 16, 75, 456, 3185, 25488, 229383, 2293840, 25232229, 302786760, 3936227867, 55107190152, 826607852265, 13225725636256, 224837335816335, 4047072044694048, 76894368849186893, 1537887376983737880, 32295634916658495459, 710503968166486900120, 16341591267829198702737
Offset: 0
-
Table[n!(1+Sum[(-1)^k k/k!,{k,0,n}]),{n,0,30}] (* Harvey P. Dale, Mar 26 2025 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*exp(-x))/(1-x)))
Showing 1-4 of 4 results.