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A096914 Number of partitions of 2*n into distinct parts with exactly two odd parts. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

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

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

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Last modified March 2 06:37 EST 2021. Contains 341744 sequences. (Running on oeis4.)