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URL: https://oeis.org/A089949

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A089949
Triangle T(n,k), read by rows, given by [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] where DELTA is the operator defined in A084938.
10
1, 0, 1, 0, 1, 2, 0, 1, 6, 6, 0, 1, 12, 34, 24, 0, 1, 20, 110, 210, 120, 0, 1, 30, 270, 974, 1452, 720, 0, 1, 42, 560, 3248, 8946, 11256, 5040, 0, 1, 56, 1036, 8792, 38338, 87504, 97296, 40320, 0, 1, 72, 1764, 20580, 129834, 463050, 920184, 930960, 362880
OFFSET
0,6
COMMENTS
Row reverse appears to be A111184. - Peter Bala, Feb 17 2017
LINKS
FORMULA
Sum_{k=0..n} x^(n-k)*T(n,k) = A111528(x, n); see A000142, A003319, A111529, A111530, A111531, A111532, A111533 for x = 0, 1, 2, 3, 4, 5, 6. - Philippe Deléham, Aug 09 2005
Sum_{k=0..n} T(n,k)*3^k = A107716(n). - Philippe Deléham, Aug 15 2005
Sum_{k=0..n} T(n,k)*2^k = A000698(n+1). - Philippe Deléham, Aug 15 2005
G.f.: A(x, y) = (1/x)*(1 - 1/(1 + Sum_{n>=1} [Product_{k=0..n-1}(1+k*y)]*x^n )). - Paul D. Hanna, Aug 16 2005
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 2;
0, 1, 6, 6;
0, 1, 12, 34, 24;
0, 1, 20, 110, 210, 120;
0, 1, 30, 270, 974, 1452, 720; ...
MATHEMATICA
m = 10;
gf = (1/x)*(1-1/(1+Sum[Product[(1+k*y), {k, 0, n-1}]*x^n, {n, 1, m}]));
CoefficientList[#, y]& /@ CoefficientList[gf + O[x]^m, x] // Flatten (* Jean-François Alcover, May 11 2019 *)
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(n==0, 1, if(k==0, 0, polcoeff(polcoeff( (1-1/(1+sum(m=1, n+k, prod(j=0, m-1, 1+j*y)*x^m)))/x +x*O(x^n), n, x)+y*O(y^k), k, y)))) \\ Paul D. Hanna, Aug 16 2005
CROSSREFS
Row sums: A003319.
Sequence in context: A331047 A390724 A264550 * A085845 A138106 A131689
KEYWORD
easy,nonn,tabl
AUTHOR
Philippe Deléham, Jan 11 2004
STATUS
approved