Search: id:A005001
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%I A005001 M1194
%S A005001 0,1,2,4,9,24,76,279,1156,5296,26443,142418,820988,5034585,
%T A005001 32679022,223578344,1606536889,12086679036,94951548840,
%U A005001 777028354999,6609770560056,58333928795428,533203744952179
%N A005001 a(0) = 0; for n>0, a(n) = Sum_k={0..n-1} Bell(k), where the Bell numbers 
               Bell(k) are given in A000110.
%C A005001 Counts rhyme schemes.
%C A005001 Row sums of triangle A137596 starting with offset 1. - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Jan 29 2008
%C A005001 With offset 1 = binomial transform of the Bell numbers, A000110 starting 
               (1, 1, 1, 2, 5, 15, 52, 203,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Dec 04 2008]
%D A005001 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005001 J. Riordan, A budget of rhyme scheme counts, pp. 455 - 465 of Second 
               International Conference on Combinatorial Mathematics, New York, 
               1978. Edited by Allan Gewirtz and Louis V. Quintas. Annals New York 
               Academy of Sciences, 319, 1979.
%H A005001 T. D. Noe, <a href="b005001.txt">Table of n, a(n) for n=0..100</a>
%H A005001 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/index.html">
               Sobalian Coefficients</a>.
%H A005001 A. F. Labossiere, <a href="http://members.lycos.co.uk/stereotomography/
               index.html">Miscellaneous</a>.
%H A005001 J. Riordan, <a href="a005000.pdf">Cached copy of paper</a>
%F A005001 a(0) = 0; for n >= 0, a(n+1) = 1 + Sum_{j=1..n} (C(n, j)-C(n, j+1))*a(j).
%F A005001 Sum_{i=1..n} Bell(i) = 1 + C(n, 2) + 2*C(n-3, 1) + 8*C(n-4, 1) + C(n-3, 
               2) + 22*C(n-5, 1) + 13*C(n-4, 2) + 52*C(n-6, 1) + 74*C(n-5, 2) + 
               10*C(n-4, 3) + 114*C(n-7, 1) + 314*C(n-6, 2) + 134*C(n-5, 3) + 3*C(n-4, 
               4) + 240*C(n-8, 1) + 1155*C(n-7, 2) + 1024*C(n-6, 3) + 134*C(n-5, 
               4) + 494*C(n-9, 1) + ..... . - Andre F. Labossiere (boronali(AT)laposte.net), 
               Feb 11 2005
%Y A005001 Partial sums of A000110, partial sums give A029761.
%Y A005001 Equals A024716(n-1) + 1.
%Y A005001 Cf. A102735, A094262, A000110, A008277, A102639, A003422, A000166, A000204, 
               A000045, A000108.
%Y A005001 Cf. A137596.
%Y A005001 Sequence in context: A009283 A125654 A141824 this_sequence A091151 A093542 
               A000667
%Y A005001 Adjacent sequences: A004998 A004999 A005000 this_sequence A005002 A005003 
               A005004
%K A005001 nonn,easy
%O A005001 0,3
%A A005001 N. J. A. Sloane (njas(AT)research.att.com).

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