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A069138
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Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1.
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0
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2, 2, 3, 2, 9, 4, 2, 21, 24, 5, 2, 45, 100, 50, 6, 2, 93, 360, 325, 90, 7, 2, 189, 1204, 1750, 840, 147, 8, 2, 381, 3864, 8505, 6300, 1862, 224, 9, 2, 765, 12100, 38850, 41706, 18522, 3696, 324, 10, 2, 1533, 37320, 170525, 255150, 159789, 47040, 6750, 450, 11
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table;
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history;
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OFFSET
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1,1
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COMMENTS
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The number of rhyme schemes for a stanza of n+1 lines with m rhyming syllables in its first n lines.
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REFERENCES
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Suggested by R. K. Guy, Mar 11, 2002.
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LINKS
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Table of n, a(n) for n=1..55.
Stephen Pollard, C.S. Peirce and the Bell Numbers, Mathematics Magazine, Vol. 76 (2003), pp. 99-106.
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FORMULA
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T(n, m) = (m+1)*S2(n, m).
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EXAMPLE
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Triangle begins:
2;
2, 3;
2, 9, 4;
2, 21, 24, 5;
2, 45, 100, 50, 6;
...
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PROG
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(PARI) T(n, m) = stirling(n, m, 2)*(m+1);
tabl(nn) = for(n=1, nn, for (k=1, n, print1(T(n, m), ", ")); print); \\ Michel Marcus, Sep 21 2017
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CROSSREFS
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Row sums give Bell numbers A000110.
Sequence in context: A177047 A016001 A016012 * A179592 A058671 A016002
Adjacent sequences: A069135 A069136 A069137 * A069139 A069140 A069141
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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N. J. A. Sloane, Apr 10 2002
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jul 01 2002
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STATUS
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approved
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