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 A050315 Main diagonal of A050314. 23
 1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 5, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also, a(n) is the number of odd multinomial coefficients n!/(k_1!...k_m!) with 1 <= k_1 <= ... <= k_m and k_1 + ... + k_m = n. - Pontus von Brömssen, Mar 23 2018 From Gus Wiseman, Mar 30 2019: (Start) Also the number of strict integer partitions of n with no binary carries. The Heinz numbers of these partitions are given by A325100. A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion. For example, the a(1) = 1 through a(15) = 15 strict integer partitions with no binary carries are: (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C) (D) (E) (F) (21) (41) (42) (43) (81) (82) (83) (84) (85) (86) (87) (52) (92) (94) (A4) (96) (61) (A1) (C1) (C2) (A5) (421) (821) (841) (842) (B4) (C3) (D2) (E1) (843) (852) (861) (942) (A41) (C21) (8421) (End) LINKS Alois P. Heinz, Table of n, a(n) for n = 0..16383 Michael Gilleland, Some Self-Similar Integer Sequences FORMULA Bell number of number of 1's in binary: a(n) = A000110(A000120(n)). MAPLE a:= n-> combinat[bell](add(i, i=convert(n, base, 2))): seq(a(n), n=0..100); # Alois P. Heinz, Apr 08 2019 MATHEMATICA binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&stableQ[#, Intersection[binpos[#1], binpos[#2]]!={}&]&]], {n, 0, 20}] (* Gus Wiseman, Mar 30 2019 *) a[n_] := BellB[DigitCount[n, 2, 1]]; a /@ Range[0, 100] (* Jean-François Alcover, May 21 2021 *) CROSSREFS Cf. A000110, A000120, A050314. Cf. A070939, A080572, A247935, A267610. Cf. A325093, A325095, A325096, A325099, A325100, A325103, A325110, A325123. Main diagonal of A307431 and of A307505. Sequence in context: A208888 A258783 A079318 * A128978 A325110 A357888 Adjacent sequences: A050312 A050313 A050314 * A050316 A050317 A050318 KEYWORD nonn AUTHOR Christian G. Bower, Sep 15 1999 STATUS approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)