A069138 Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1.

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

Offset

1,1

Comments

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

References

Suggested by R. K. Guy, Mar 11, 2002.

Links

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.

Formula

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

Example

Triangle begins:
2;
2,  3;
2,  9,   4;
2, 21,  24,  5;
2, 45, 100, 50, 6;
...

Prog

(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

Crossrefs

Row sums give Bell numbers A000110.

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

Sequence in context: A334490 A016001 A016012 * A179592 A058671 A016002

Adjacent sequences: A069135 A069136 A069137 * A069139 A069140 A069141

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Apr 10 2002

Extensions

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

Status

approved