login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005896 Weighted count of partitions with odd parts.
(Formerly M2338)
3
0, 0, 0, 1, 1, 3, 4, 7, 9, 14, 19, 26, 34, 45, 59, 76, 96, 121, 153, 189, 234, 288, 353, 428, 519, 625, 752, 900, 1073, 1274, 1512, 1784, 2101, 2470, 2894, 3382, 3946, 4590, 5330, 6179, 7144, 8246, 9505, 10931, 12552, 14396, 16476, 18831, 21495 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

Andrews, George E. Ramanujan's "lost" notebook. V. Euler's partition identity. Adv. in Math. 61 (1986), no. 2, 156-164.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

FORMULA

G.f.: Sum_{n=0..inf} {S(q)-1/((1-q)(1-q^3)...(1-q^(2n+1)))}, where S(q) = g.f. for A000009.

MATHEMATICA

max = 48; f[n_, x_] := Product[ 1/(1-x^(2k+1)), {k, 0, n}]; g[x_] = Sum[ f[max/2, x] - f[n, x], {n, 0, max/2}]; CoefficientList[ Series[ g[x], {x, 0, max}], x] (* Jean-Fran├žois Alcover, Nov 17 2011, after g.f. *)

PROG

(PARI) /* set "infinity" */ oo = 50; /* G.f. for partitions with odd parts: */ Q(n, q) = prod(k=0, n, 1/(1-q^(2*k+1)), 1+q*O(q^oo)); /* G.f. for A000009: */ Sq = Q(oo/2, q); /* G.f. for A005896: */ Sq0 = sum(n=0, oo/2, Sq-Q(n, q)); for(n=0, 48, print1(polcoeff(Sq0, n)", "))

CROSSREFS

Cf. A000009, A005895, A003406.

Sequence in context: A098390 A266769 A008763 * A147953 A163468 A069183

Adjacent sequences:  A005893 A005894 A005895 * A005897 A005898 A005899

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

More terms from Michael Somos.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 11:39 EDT 2018. Contains 316359 sequences. (Running on oeis4.)