0,3

Counts rhyme schemes.

Row sums of triangle A137596 starting with offset 1. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 29 2008

With offset 1 = binomial transform of the Bell numbers, A000110 starting (1, 1, 1, 2, 5, 15, 52, 203,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 04 2008]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

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

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

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: A009283 A125654 A141824 this_sequence A091151 A093542 A000667

Adjacent sequences: A004998 A004999 A005000 this_sequence A005002 A005003 A005004

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).