The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A301767 Number of ways to choose a constant rooted partition of each part in a strict rooted partition of n. 1
 1, 1, 1, 3, 4, 7, 9, 15, 21, 32, 45, 59, 89, 117, 162, 225, 309, 394, 538, 707, 929, 1240, 1613, 2055, 2677, 3517, 4439, 5724, 7288, 9222, 11671, 14809, 18480, 23226, 29138, 36501, 45373, 56438, 69920, 86426, 106715, 131171, 161428, 197717, 242301, 295888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A rooted partition of n is an integer partition of n - 1. LINKS FORMULA O.g.f.: Product_{n>0} (1 + d(n-1) x^n) where d(n) = A000005(n) and d(0) = 1. EXAMPLE The a(7) = 9 rooted twice-partitions: (5), (11111), (4)(), (22)(), (1111)(), (3)(1), (111)(1), (2)(1)(), (11)(1)(). MATHEMATICA Table[Sum[Product[If[k===1, 1, DivisorSigma[0, k-1]], {k, ptn}], {ptn, Select[IntegerPartitions[n-1], UnsameQ@@#&]}], {n, 50}] CROSSREFS Cf. A002865, A032305, A063834, A093637, A279786, A296131, A301422, A301462, A301467, A301480, A301706. Sequence in context: A241335 A158911 A086772 * A169898 A281734 A086336 Adjacent sequences:  A301764 A301765 A301766 * A301768 A301769 A301770 KEYWORD nonn AUTHOR Gus Wiseman, Mar 26 2018 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)