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Search: id:A005001
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| A005001 |
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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.
(Formerly M1194)
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+0
8
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| 0, 1, 2, 4, 9, 24, 76, 279, 1156, 5296, 26443, 142418, 820988, 5034585, 32679022, 223578344, 1606536889, 12086679036, 94951548840, 777028354999, 6609770560056, 58333928795428, 533203744952179
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Counts rhyme schemes.
Row sums of triangle A137596 starting with offset 1. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 29 2008
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REFERENCES
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
A. F. Labossiere, Sobalian Coefficients.
A. F. Labossiere, Miscellaneous.
J. Riordan, Cached copy of paper
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FORMULA
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a(0) = 0; for n >= 0, a(n+1) = 1 + Sum_{j=1..n} (C(n, j)-C(n, j+1))*a(j).
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
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CROSSREFS
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Partial sums of A000110, partial sums give A029761.
Equals A024716(n-1) + 1.
Cf. A102735, A094262, A000110, A008277, A102639, A003422, A000166, A000204, A000045, A000108.
Cf. A137596.
Sequence in context: A092236 A009283 A125654 this_sequence A091151 A093542 A000667
Adjacent sequences: A004998 A004999 A005000 this_sequence A005002 A005003 A005004
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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