A344317
a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 1.
Original entry on oeis.org
1, 2, 6, 19, 80, 401, 2412, 16885, 135088, 1215793, 12157940, 133737341, 1604848104, 20863025353, 292082354956, 4381235324341, 70099765189472, 1191696008221025, 21450528147978468, 407560034811590893, 8151200696231817880, 171175214620868175481
Offset: 0
A344419
a(n) = n*a(n-1) + n^(n mod 2), a(0) = 0.
Original entry on oeis.org
0, 1, 3, 12, 49, 250, 1501, 10514, 84113, 757026, 7570261, 83272882, 999274585, 12990569618, 181867974653, 2728019619810, 43648313916961, 742021336588354, 13356384058590373, 253771297113217106, 5075425942264342121, 106583944787551184562, 2344846785326126060365
Offset: 0
A344495
a(0)=1; for n>0 a(n)=(a(n-1) + n) * n if n is odd, a(n-1)*n + n otherwise.
Original entry on oeis.org
1, 2, 6, 27, 112, 585, 3516, 24661, 197296, 1775745, 17757460, 195332181, 2343986184, 30471820561, 426605487868, 6399082318245, 102385317091936, 1740550390563201, 31329907030137636, 595268233572615445, 11905364671452308920, 250012658100498487761, 5500278478210966730764
Offset: 0
a(0) = 1;
a(1) = (a(0)+1)*1 = (1+1)*1 = 2 ;
a(2) = a(1)*2+2 = (2*2)+2 = 6 ;
a(3) = (a(2)+3)*3 = (6+3)*3 = 9 ;
-
a:= proc(n) a(n):= n*a(n-1) + n^(1+(n mod 2)) end: a(0):= 1:
seq(a(n), n=0..22); # Alois P. Heinz, May 21 2021
-
a[0] = 1; a[n_] := a[n] = n*(a[n - 1] + If[OddQ[n], n, 1]); Array[a, 30, 0] (* Amiram Eldar, May 21 2021 *)
A344935
a(0)=1; for n > 0, a(n) = n*(a(n-1) + i^(n-1)) if n is odd, n*a(n-1) + i^n otherwise, where i = sqrt(-1).
Original entry on oeis.org
1, 2, 3, 6, 25, 130, 779, 5446, 43569, 392130, 3921299, 43134278, 517611337, 6728947394, 94205263515, 1413078952710, 22609263243361, 384357475137154, 6918434552468771, 131450256496906630, 2629005129938132601, 55209107728700784642, 1214600370031417262123
Offset: 0
a(0) = 1;
a(1) = 1*(a(0) + i^(1-1)) = 2;
a(2) = 2*a(1) + i^2 = 3;
a(3) = 3*(a(2) + i^2) = 6;
a(4) = 4*a(3) + i^4 = 25.
-
A344935 := proc(n)
option remember ;
if n = 0 then
1;
elif type(n,'odd') then
n*(procname(n-1)+I^(n-1)) ;
else
n*procname(n-1)+I^n ;
end if;
simplify(%) ;
end proc:
seq(A344935(n),n=0..40) ; # R. J. Mathar, Aug 19 2022
-
a[0] = 1; a[n_] := a[n] = If[OddQ[n], n*(a[n - 1] + I^(n - 1)), n*a[n - 1] + I^n]; Array[a, 30, 0] (* Amiram Eldar, Jun 03 2021 *)
-
a(n) = if (n==0, 1, if (n%2, n*(a(n-1) + I^(n-1)), n*a(n-1) + I^n)); \\ Michel Marcus, Jun 05 2021
A344496
a(0)=0; for n > 0, a(n) = a(n-1)*n + n if n is odd, (a(n-1) + n)*n otherwise.
Original entry on oeis.org
0, 1, 6, 21, 100, 505, 3066, 21469, 171816, 1546353, 15463630, 170099941, 2041199436, 26535592681, 371498297730, 5572474465965, 89159591455696, 1515713054746849, 27282834985443606, 518373864723428533, 10367477294468571060, 217717023183839992281, 4789774510044479830666
Offset: 0
a(0) = 0;
a(1) = a(0)*1 + 1 = 0 + 1 = 1;
a(2) = (a(1)+2)* 2 = (1 + 2)*2 = 6;
a(3) = a(2)*3 + 3 = 6*3 + 3 = 21;
a(4) = (a(3)+4)* 4 = (21 + 4)*4 = 100.
-
a:= proc(n) a(n):= n*a(n-1) + n^(2-(n mod 2)) end: a(0):= 0:
seq(a(n), n=0..22); # Alois P. Heinz, May 21 2021
-
a[0] = 0; a[n_] := a[n] = n * (a[n - 1] + If[OddQ[n], 1, n]); Array[a, 30, 0] (* Amiram Eldar, May 21 2021 *)
Table[n*(-1 + 3*E*Gamma[n,1] + (n-1)*Subfactorial[n-2])/2, {n, 0, 30}] (* Vaclav Kotesovec, Jun 05 2021 *)
Showing 1-5 of 5 results.