A093935 a(1) = 1, a(n+1) = a(n) + n*(a(1) + a(2) + ... + a(n)).

1, 2, 8, 41, 249, 1754, 14084, 127057, 1272625, 14015014, 168323364, 2189619553, 30670104577, 460235322854, 7366138539416, 125257398648401, 2255126454472401, 42855262052316218, 857238357862313360

Offset: 1

Author

Amarnath Murthy, Apr 26 2004

Keywords

• nonn

Programs

Maple

a[1]:=1:a[2]:=2: for n from 2 to 30 do a[n+1]:=((n^2+n-1)*a[n]-n*a[n-1])/(n-1) od:seq(a[n],n=1..23); # Emeric Deutsch, Apr 18 2005

Mathematica

RecurrenceTable[{a[1]==1, a[2]==2, a[n+1] == ((n^2 + n - 1)*a[n] - n*a[n-1])/(n-1)},a,{n,1,20}] (* Vaclav Kotesovec, Jul 13 2021 *)

Formula

a(1)=1, a(2)=2, a(n+1) = ((n^2 + n - 1)*a(n) - n*a(n-1))/(n-1) (n >= 2). - Emeric Deutsch, Apr 18 2005

a(n) ~ c * n * n!, where c = BesselJ(2,2) = 0.3528340286156377191506207876191884610951482075010678369927893147532331585216... - Vaclav Kotesovec, Jul 13 2021, updated Sep 24 2023

Extensions

More terms from Emeric Deutsch, Apr 18 2005