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Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1.
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%I #13 Feb 09 2023 05:57:27

%S 2,2,3,2,9,4,2,21,24,5,2,45,100,50,6,2,93,360,325,90,7,2,189,1204,

%T 1750,840,147,8,2,381,3864,8505,6300,1862,224,9,2,765,12100,38850,

%U 41706,18522,3696,324,10,2,1533,37320,170525,255150,159789,47040,6750,450,11

%N Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1.

%C The number of rhyme schemes for a stanza of n+1 lines with m rhyming syllables in its first n lines.

%D Suggested by _R. K. Guy_, Mar 11, 2002.

%H Stephen Pollard, <a href="http://www.jstor.org/stable/3219302">C.S. Peirce and the Bell Numbers</a>, Mathematics Magazine, Vol. 76 (2003), pp. 99-106.

%F T(n, m) = (m+1)*S2(n, m).

%e Triangle begins:

%e 2;

%e 2, 3;

%e 2, 9, 4;

%e 2, 21, 24, 5;

%e 2, 45, 100, 50, 6;

%e ...

%o (PARI) T(n, m) = stirling(n, m, 2)*(m+1);

%o tabl(nn) = for(n=1, nn, for (k=1, n, print1(T(n, m), ", ")); print); \\ _Michel Marcus_, Sep 21 2017

%Y Row sums give Bell numbers A000110.

%Y Cf. A360174 (Stirling1 counterpart), A360205 (Lah counterpart).

%K nonn,tabl,easy

%O 1,1

%A _N. J. A. Sloane_, Apr 10 2002

%E More terms from Larry Reeves (larryr(AT)acm.org), Jul 01 2002