0,2

Equals row sums of triangle A163946 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 06 2009]

G.f. satisfies: (1-x)*A(x-x^2) = 1 + x*A(x). G.f. satisfies: A(x) = C(x) + x*C(x)^2*A(x*C(x)), where C(x) is the Catalan function (A000108). a(n) = A000108(n) + Sum_{k=0..n-1} a(k)*C(2*n-k-1,n-k-1)*(k+2)/(n+1) for n>=0; eigensequence (shift left) of the Catalan triangle A033184. [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 13 2008]

The Bell numbers can be generated by;

1

1 2

2 3 5

5 7 10 15

where the Bell numbers are the last entry on each line. This last entry is the first entry on the next line and then the entries of the previous line are added, e.g. 7=5+2, 10=7+3, 15=10+5.

This version adds ALL of the entries in the previous column to the new entry.

1

1 2

2 4 6

6 10 16 22

where 10=6+2+1+1, 16=10+2+4, 22=16+6

(PARI) { v=vector(20); for (i=1, 20, v[i]=vector(i)); v[1][1]=1; for (i=2, 20, v[i][1]=v[i-1][i-1]; for (j=2, i, v[i][j]=v[i][j-1]+sum(k=j-1, i-1, v[k][j-1]))); for (i=1, 20, print1(", "v[i][i])) }

(PARI) {a(n)=binomial(2*n, n)/(n+1)+sum(k=0, n-1, a(k)*binomial(2*n-k-1, n-k-1)*(k+2)/(n+1))} (PARI) {a(n)=local(A=1+x*O(x^n), C=serreverse(x-x^2+x^2*O(x^n))/x); for(i=0, n, A=C+x*C^2*subst(A, x, x*C)); polcoeff(A, n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 13 2008]

Close to A074664

Cf. A000110 (Bell Numbers).

Cf. A033184, A000108. [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 13 2008]

A163946 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 06 2009]

Sequence in context: A124294 A124295 A074664 this_sequence A150274 A109317 A109153

Adjacent sequences: A091765 A091766 A091767 this_sequence A091769 A091770 A091771

nonn

Jon Perry (perry(AT)globalnet.co.uk), Mar 06 2004