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A100824 Number of partitions of n with at most one odd part. 2
1, 1, 1, 2, 2, 4, 3, 7, 5, 12, 7, 19, 11, 30, 15, 45, 22, 67, 30, 97, 42, 139, 56, 195, 77, 272, 101, 373, 135, 508, 176, 684, 231, 915, 297, 1212, 385, 1597, 490, 2087, 627, 2714, 792, 3506, 1002, 4508, 1255, 5763, 1575, 7338, 1958, 9296, 2436, 11732, 3010, 14742 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (1+x/(1-x^2))/Product(1-x^(2*i), i=1..infinity). More generally, g.f. for number of partitions of n with at most k odd parts is (1+Sum(x^i/Product(1-x^(2*j), j=1..i), i=1..k))/Product(1-x^(2*i), i=1..infinity).

a(n) ~ exp(sqrt(n/3)*Pi) / (2*sqrt(3)*n) if n is even and a(n) ~ exp(sqrt(n/3)*Pi) / (2*Pi*sqrt(n)) if n is odd. - Vaclav Kotesovec, Mar 07 2016

MAPLE

seq(coeff(convert(series((1+x/(1-x^2))/mul(1-x^(2*i), i=1..100), x, 100), polynom), x, n), n=0..60); (C. Ronaldo)

MATHEMATICA

nmax = 50; CoefficientList[Series[(1+x/(1-x^2)) * Product[1/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2016 *)

CROSSREFS

Cf. A000041, A000070, A008951, A000097, A000098, A000710.

Sequence in context: A007439 A238622 A096441 * A163227 A238779 A239832

Adjacent sequences:  A100821 A100822 A100823 * A100825 A100826 A100827

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jan 13 2005

EXTENSIONS

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005

STATUS

approved

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Last modified February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)