A267008 Expansion of Product_{k>=1} (1 + (k+1)*x^k).

1, 2, 3, 10, 13, 28, 58, 90, 146, 260, 481, 688, 1168, 1748, 2863, 4726, 6938, 10412, 16140, 23746, 35702, 55812, 79032, 116758, 168779, 247006, 350310, 513410, 744286, 1045466, 1485685, 2098780, 2935416, 4137878, 5746618, 8027612, 11343706, 15487222, 21418682

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
     `if`(n=0, 1, b(n, i-1)+(1+i)*b(n-i, min(n-i, i-1))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..42);  # Alois P. Heinz, Aug 15 2019

Mathematica

nmax = 50; CoefficientList[Series[Product[1+(k+1)*x^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; poly = ConstantArray[0, nmax+1]; poly[[1]] = 1; poly[[2]] = 2; Do[Do[poly[[j+1]] += (k+1)*poly[[j-k+1]], {j, nmax, k, -1}]; , {k, 2, nmax}]; poly

Crossrefs

Cf. A022629, A074141, A267007.

Sequence in context: A004688 A024852 A023856 * A129315 A171126 A299205

Adjacent sequences: A267005 A267006 A267007 * A267009 A267010 A267011

Keyword

nonn

Author

Vaclav Kotesovec, Jan 08 2016

Status

approved