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A221971 G.f.: A(x,y) = Sum_{n>=0} n! * x^n*y^n * Product_{k=1..n} (1 + k*x) / (1 + k*x*y + k^2*x^2*y). 2
1, 0, 1, 0, 1, 1, 0, 0, 4, 1, 0, 0, 3, 11, 1, 0, 0, 0, 27, 26, 1, 0, 0, 0, 17, 148, 57, 1, 0, 0, 0, 0, 278, 646, 120, 1, 0, 0, 0, 0, 155, 2590, 2481, 247, 1, 0, 0, 0, 0, 0, 4073, 18304, 8805, 502, 1, 0, 0, 0, 0, 0, 2073, 58427, 109699, 29682, 1013, 1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,9
LINKS
FORMULA
Row sums equal A208237.
Central terms equal A110501, the Genocchi numbers of first kind (unsigned).
Columns sums equal A005439, the Genocchi numbers of second kind.
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 0, 4, 1;
0, 0, 3, 11, 1;
0, 0, 0, 27, 26, 1;
0, 0, 0, 17, 148, 57, 1;
0, 0, 0, 0, 278, 646, 120, 1;
0, 0, 0, 0, 155, 2590, 2481, 247, 1;
0, 0, 0, 0, 0, 4073, 18304, 8805, 502, 1;
0, 0, 0, 0, 0, 2073, 58427, 109699, 29682, 1013, 1;
0, 0, 0, 0, 0, 0, 80712, 614819, 590254, 96648, 2036, 1;
0, 0, 0, 0, 0, 0, 38227, 1665829, 5340996, 2948040, 307255, 4083, 1; ...
PROG
(PARI) {T(n, k)=polcoeff(polcoeff(sum(m=0, n, m!*x^m*y^m*prod(k=1, m, (1+k*x)/(1+k*x*y+k^2*x^2*y +x*O(x^n)))), n, x), k, y)}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))
CROSSREFS
Cf. A208237 (row sums), A110501 (central terms), A005439 (column sums), A136126.
Sequence in context: A049763 A328290 A182878 * A297785 A334702 A345300
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Feb 01 2013
STATUS
approved

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Last modified March 28 09:02 EDT 2024. Contains 371237 sequences. (Running on oeis4.)