A265951
Expansion of Product_{k>=1} 1/(1 - 2*k*x^k).
Original entry on oeis.org
1, 2, 8, 22, 68, 170, 484, 1166, 3048, 7274, 18000, 41806, 100684, 229258, 535692, 1206230, 2758944, 6123650, 13798088, 30284894, 67272756, 146426002, 321513284, 693944814, 1510245960, 3236648578, 6985572672, 14885926182, 31904642348, 67618415690
Offset: 0
-
b:= proc(n, i) option remember; `if`(n=0 or i=1,
2^n, b(n, i-1) +i*2*b(n-i, min(n-i, i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..32); # Alois P. Heinz, Aug 23 2019
-
nmax=40; CoefficientList[Series[Product[1/(1-2*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
A265974
Expansion of Product_{k>=1} 1/(1 - 3*k*x^k).
Original entry on oeis.org
1, 3, 15, 54, 210, 699, 2484, 7995, 26610, 84186, 269940, 839238, 2634579, 8098194, 25032282, 76388265, 233791104, 709501596, 2157488730, 6523204836, 19747491810, 59558682132, 179762506329, 541222906812, 1630300772106, 4902697929306, 14748249476553
Offset: 0
-
b:= proc(n, i) option remember; `if`(n=0 or i=1,
3^n, b(n, i-1) +i*3*b(n-i, min(n-i, i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..32); # Alois P. Heinz, Aug 23 2019
-
nmax=40; CoefficientList[Series[Product[1/(1-3*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
A265975
Expansion of Product_{k>=1} 1/(1 - 4*k*x^k).
Original entry on oeis.org
1, 4, 24, 108, 512, 2164, 9464, 39004, 163008, 663588, 2713752, 10954764, 44328512, 178160724, 716821752, 2874497660, 11532111232, 46187508676, 185028540696, 740595436652, 2964628293504, 11862432443764, 47467812675320, 189902835709212, 759756868215872
Offset: 0
-
b:= proc(n, i) option remember; `if`(n=0 or i=1,
4^n, b(n, i-1) +i*4*b(n-i, min(n-i, i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..32); # Alois P. Heinz, Aug 23 2019
-
nmax=40; CoefficientList[Series[Product[1/(1-4*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Showing 1-3 of 3 results.