|
Search: id:A038455
|
|
| |
|
| 1, 3, 1, 20, 9, 1, 210, 107, 18, 1, 3024, 1650, 335, 30, 1, 55440, 31594, 7155, 805, 45, 1, 1235520, 725592, 176554, 22785, 1645, 63, 1, 32432400, 19471500, 4985316, 705649, 59640, 3010, 84, 1, 980179200, 598482000, 159168428, 24083892, 2267769
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
i) This triangle gives the nonvanishing entries of the Jabotinsky matrix for F(z)= c(z) with c(z) the g.f. for the Catalan numbers A000108. (Notation of F(z) as in Knuth's paper).
ii) E(n,x) := sum(a(n,m)*x^m,m=1..n), E(0,x)=1, are exponential convolution polynomials: E(n,x+y) = sum(binomial(n,k)*E(k,x)*E(n-k,y),k=0..n) (cf. Knuth's paper with E(n,x)= n!*F(n,x).)
iii) Explicit formula: see Knuth's paper for f(n,m) formula with f(k)= A006963(k+1).
|
|
REFERENCES
|
D. E. Knuth, Convolution polynomials, The Mathematica J., 2.1 (1992) 67-78.
|
|
LINKS
|
J.-C. Novelli and J.-Y. Thibon, Noncommutative Symmetric Functions and Lagrange Inversion
|
|
FORMULA
|
a(n, 1) = A006963(n+1)=(2*n-1)!/n!, n >= 1; a(n, m) = sum(binomial(n-1, j-1)*A006963(j+1)*a(n-j, m-1), j=1..n-m+1), n >= m >= 2.
E.g.f.: ((1-sqrt(1-4*x))/x/2)^y. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 02 2003
|
|
CROSSREFS
|
A006963, A000108.
Cf. A001761, A039619, A039646.
Sequence in context: A027537 A002380 A073676 this_sequence A067802 A139723 A030042
Adjacent sequences: A038452 A038453 A038454 this_sequence A038456 A038457 A038458
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
|
|
|
Search completed in 0.105 seconds
|
