This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A069138 #16 Aug 02 2025 17:04:54 %S A069138 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 A069138 1750,840,147,8,2,381,3864,8505,6300,1862,224,9,2,765,12100,38850, %U A069138 41706,18522,3696,324,10,2,1533,37320,170525,255150,159789,47040,6750,450,11 %N A069138 Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1. %C A069138 The number of rhyme schemes for a stanza of n+1 lines with m rhyming syllables in its first n lines. %D A069138 Suggested by _R. K. Guy_, Mar 11 2002. %H A069138 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 A069138 T(n, m) = (m+1)*S2(n, m). %e A069138 Triangle begins: %e A069138 2; %e A069138 2, 3; %e A069138 2, 9, 4; %e A069138 2, 21, 24, 5; %e A069138 2, 45, 100, 50, 6; %e A069138 ... %o A069138 (PARI) T(n, m) = stirling(n, m, 2)*(m+1); %o A069138 tabl(nn) = for(n=1, nn, for (k=1, n, print1(T(n, m), ", ")); print); \\ _Michel Marcus_, Sep 21 2017 %Y A069138 Row sums give Bell numbers A000110. %Y A069138 Cf. A360174 (Stirling1 counterpart), A360205 (Lah counterpart). %K A069138 nonn,tabl,easy %O A069138 1,1 %A A069138 _N. J. A. Sloane_, Apr 10 2002 %E A069138 More terms from Larry Reeves (larryr(AT)acm.org), Jul 01 2002