A096914 Number of partitions of 2*n into distinct parts with exactly two odd parts.

1, 2, 4, 7, 11, 17, 25, 36, 50, 69, 93, 124, 163, 212, 273, 349, 442, 556, 695, 863, 1066, 1310, 1602, 1950, 2364, 2854, 3433, 4115, 4916, 5854, 6951, 8229, 9716, 11442, 13441, 15752, 18419, 21490, 25021, 29074, 33718, 39031, 45101, 52024, 59910

Offset

2,2

Links

Table of n, a(n) for n=2..46.

Amrik Singh Nimbran and Paul Levrie, Series of the form Sum {a_n*binomial(2n, n)}, Math. Student (2023) Vol. 92, Nos. 3-4, 155-173. See p. 9.

Formula

G.f. for number of partitions of n into distinct parts with exactly k odd parts is x^(k^2)*Product(1+x^(2*m), m=1..infinity)/Product(1-x^(2*m), m=1..k).

a(n) ~ 3^(3/4) * exp(Pi*sqrt(n/3)) * n^(1/4) / (2*Pi^2). - Vaclav Kotesovec, May 29 2018

Mathematica

Drop[ Union[ CoefficientList[ Series[x^4* Product[1 + x^(2m), {m, 1, 50}] / Product[1 - x^(2m), {m, 1, 2}], {x, 0, 920}], x]], 1] (* Robert G. Wilson v, Aug 21 2004 *)
nmax = 50; Drop[CoefficientList[Series[(x^2/(1 - x - x^2 + x^3)) * Product[1 + x^m, {m, 1, nmax}], {x, 0, nmax}], x], 2] (* Vaclav Kotesovec, May 29 2018 *)

Crossrefs

Cf. A000009, A036469, A015128.

Sequence in context: A034379 A007000 A073472 * A004250 A289060 A194805

Adjacent sequences: A096911 A096912 A096913 * A096915 A096916 A096917

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 18 2004

Extensions

More terms from Robert G. Wilson v, Aug 21 2004

Status

approved