A258457 Number of partitions of n into parts of exactly 2 sorts which are introduced in ascending order.

1, 4, 12, 30, 72, 160, 351, 743, 1561, 3219, 6616, 13456, 27312, 55139, 111166, 223472, 448902, 900305, 1804838, 3615137, 7239325, 14490368, 29000050, 58025059, 116090823, 232234573, 464554483, 929220024, 1858618215, 3717468189, 7435305664, 14871092926

Offset

2,2

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Formula

a(n) ~ c * 2^n, where c = 1/Product_{n>=2} (1-1/2^n) = 1/(2*A048651) = 1.7313733097275318... . - Vaclav Kotesovec, Jun 01 2015

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
    end:
T:= (n, k)-> add(b(n$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 2):
seq(a(n), n=2..35);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, k*b[n - i, i, k]]]];
T[n_, k_] := Sum[b[n, n, k - i]*(-1)^i/(i!*(k - i)!), {i, 0, k}];
a[n_] := T[n, 2];
a /@ Range[2, 35] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=2 of A256130.

Sequence in context: A006802 A068055 A221855 * A279152 A317780 A274217

Adjacent sequences: A258454 A258455 A258456 * A258458 A258459 A258460

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved