This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A279374 Number of ways to choose an odd partition of each part of an odd partition of 2n+1. 9
 1, 3, 6, 15, 37, 80, 183, 428, 893, 1944, 4223, 8691, 18128, 37529, 75738, 153460, 308829, 612006, 1211097, 2386016, 4648229, 9042678, 17528035, 33645928, 64508161, 123178953, 233709589, 442583046, 834923483, 1567271495, 2935406996, 5481361193, 10191781534 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS An odd partition is an integer partition of an odd number with an odd number of parts, all of which are odd. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..4919 Gus Wiseman, "Twice-odd partitions of n=9." EXAMPLE The a(3)=15 ways to choose an odd partition of each part of an odd partition of 7 are: ((7)), ((511)), ((331)), ((31111)), ((1111111)), ((5)(1)(1)), ((311)(1)(1)), ((11111)(1)(1)), ((3)(3)(1)), ((3)(111)(1)), ((111)(3)(1)), ((111)(111)(1)), ((3)(1)(1)(1)(1)), ((111)(1)(1)(1)(1)), ((1)(1)(1)(1)(1)(1)(1)). MAPLE g:= proc(n) option remember; `if`(n=0, 1, add(add(d*       [0, 2, 0, 1\$4, 2, 0, 2, 1\$4, 0, 2][1+irem(d, 16)],       d=numtheory[divisors](j))*g(n-j), j=1..n)/n)     end: b:= proc(n, i, t) option remember;       `if`(n=0, t, `if`(i<1, 0, b(n, i-2, t)+       `if`(i>n, 0, b(n-i, i, 1-t)*g((i-1)/2))))     end: a:= n-> b(2*n+1\$2, 0): seq(a(n), n=0..35);  # Alois P. Heinz, Dec 12 2016 MATHEMATICA nn=20; Table[SeriesCoefficient[Product[1/(1-PartitionsQ[k]x^k), {k, 1, 2n-1, 2}], {x, 0, 2n-1}], {n, nn}] CROSSREFS Cf. A000009 (strict partitions), A078408 (odd partitions), A063834, A271619, A279375. Sequence in context: A099323 A058534 A063778 * A087124 A086326 A098701 Adjacent sequences:  A279371 A279372 A279373 * A279375 A279376 A279377 KEYWORD nonn AUTHOR Gus Wiseman, Dec 11 2016 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.

Last modified October 23 05:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)