

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
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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
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



FORMULA



MAPLE

a:= n> combinat[bell](add(i, i=convert(n, base, 2))):


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]];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



