OFFSET
1,5
COMMENTS
For example, the Euler transform of 1,3,6,... is 1,1,4,10,26,59,141,... (A000294) differing slightly from A000293 which counts the solid partitions.
The NAME does not reproduce the DATA, COMMENTS, or EXAMPLES. - R. J. Mathar, Jul 19 2017
The binomial transforms of the rows form the rows of A289656. - N. J. A. Sloane, Jul 19 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)
N. J. A. Sloane, Transforms
EXAMPLE
Row 6 is 1 10 27 29 12 1 generating 1 11 48 141 ... (A008780) the seventh term in the Euler transforms of 1,1,1,...; 1,2,3,...; 1,3,6,... 1,4,10,... etc.
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 4, 4, 1;
1, 6, 11, 7, 1;
1, 10, 27, 29, 12, 1;
1, 14, 57, 96, 72, 21, 1;
1, 21, 117, 277, 319, 176, 38, 1;
...
PROG
(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
T(n)={my(u=vector(n-1, k, EulerT(vector(n, j, binomial(j+k-2, k-1))))); vector(n, n, vector(n, k, k--; (-1)^k + sum(j=1, k, (-1)^(k-j)*binomial(k, j)*u[j][n]))) }
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Oct 02 2025
CROSSREFS
KEYWORD
AUTHOR
Alford Arnold, Feb 22 2006
EXTENSIONS
a(37) onwards from Andrew Howroyd, Oct 02 2025
STATUS
approved
