OFFSET
2,5
REFERENCES
J. Riordan, The blossoming of Schroeder's fourth problem, Acta Math., 137 (1976), 1-16.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1276
FORMULA
A001678(n) = Sum_{i=2..n-2} T(i, n-1-i) for n >= 3. - Marko Riedel, Mar 29 2021
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 2;
1, 3, 5, 3;
1, 4, 10, 12, 6;
1, 5, 16, 29, 28, 11;
1, 6, 24, 57, 84, 66, 23;
1, 7, 33, 99, 192, 231, 157, 46;
1, 8, 44, 157, 382, 615, 634, 373, 98;
...
PROG
(PARI)
EulerMT(u)={my(n=#u, p=x*Ser(u), vars=variables(p)); Vec(exp( sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i ))-1)}
A(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n]=y*EulerMT(v[1..n])[n]); apply(p -> Vecrev(p/y), v[2..n])}
{ my(T=A(10)); for(n=1, #T, print(T[n])) } \\ Andrew Howroyd, Sep 01 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, May 29 2005
EXTENSIONS
Name clarified and terms a(38) and beyond from Andrew Howroyd, Sep 01 2018
STATUS
approved