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A046757
Triangle of coefficients of certain polynomials (exponents in decreasing order).
1
1, 2, 1, 5, 5, 1, 30, 30, 10, 1, 272, 272, 102, 17, 1, 3250, 3250, 1300, 260, 26, 1, 47952, 47952, 19980, 4440, 555, 37, 1, 840350, 840350, 360150, 85750, 12250, 1050, 50, 1, 17039360, 17039360, 7454720, 1863680, 291200, 29120, 1820, 65, 1, 392203458
OFFSET
0,2
FORMULA
a(n, n) = 1, a(n, m) = (1+n^2)*binomial(n, m)*n^(n-m-2), n>m >= 0, else 0.
EXAMPLE
Triangle begins:
{1};
{2,1};
{5,5,1};
{30,30,10,1};
{272,272,102,17,1};
....
E.g. third row {5,5,1} corresponds to polynomial q(3,x)= 5*x^2+5*x+1.
CROSSREFS
x*p(k-1, -x)/q(k, -x), with the row polynomials p(n, x) from triangle A033842(n, m) is for k=1..5 g.f. for A000079 (powers of two), A039717, A043553, A045624, A046088, respectively.
Sequence in context: A248727 A270250 A204119 * A248905 A118244 A108410
KEYWORD
easy,nonn,tabl
STATUS
approved