A117276 Number of 1's in all partitions of n with no even parts repeated.

0, 1, 2, 4, 7, 11, 17, 26, 38, 54, 76, 105, 143, 193, 257, 339, 444, 576, 742, 950, 1208, 1528, 1923, 2407, 2999, 3721, 4597, 5657, 6937, 8476, 10322, 12532, 15168, 18306, 22034, 26450, 31672, 37835, 45091, 53619, 63625, 75341, 89037, 105023, 123647

Offset

0,3

Comments

a(n)=Sum(k*A117274(n,k),k=0..n).

Links

Table of n, a(n) for n=0..44.

Formula

G.f.: x*product((1+x^(2j))/(1-x^(2j-1)), j=1..infinity)/(1-x).

a(n) ~ exp(sqrt(n/2)*Pi) / (2^(5/4)*Pi*n^(1/4)). - Vaclav Kotesovec, Mar 07 2016

G.f.: (x/(1 - x))*Product_{k>=1} (1 - x^(4*k))/(1 - x^k). - Ilya Gutkovskiy, May 15 2018

Example

a(5)=11 because the partitions of 5 with no even parts repeated are [5],[4,1],[3,2],[3,1,1],[2,1,1,1] and [1,1,1,1,1] and they have a total number 0+1+0+2+3+5=11 parts equal to 1.

Maple

g:=x*product((1+x^(2*j))/(1-x^(2*j-1)), j=1..35)/(1-x): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..47);

Mathematica

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

Crossrefs

Cf. A001935, A117274.

Sequence in context: A342492 A280962 A096967 * A035295 A289010 A006999

Adjacent sequences: A117273 A117274 A117275 * A117277 A117278 A117279

Keyword

nonn

Author

Emeric Deutsch, Mar 06 2006

Status

approved