OFFSET
1,2
COMMENTS
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..300
FORMULA
a(n) ~ (exp(2) - (-1)^n) * sqrt(3/Pi) * n^(n - 1/2) / 2. - Vaclav Kotesovec, Dec 27 2018
EXAMPLE
Triangle A322229, where row n gives coefficients in Product_{k=1..n} (k + x + (n+1-k)*x^2), begins
1;
1, 1, 1;
2, 3, 6, 3, 2;
6, 11, 32, 27, 32, 11, 6;
24, 50, 189, 210, 350, 210, 189, 50, 24;
120, 274, 1269, 1689, 3594, 2915, 3594, 1689, 1269, 274, 120;
720, 1764, 9652, 14651, 37750, 37457, 58156, 37457, 37750, 14651, 9652, 1764, 720;
5040, 13068, 82396, 138473, 417780, 481074, 896412, 714483, 896412, 481074, 417780, 138473, 82396, 13068, 5040; ...
in which the coefficient of x^(n-1) in row n for n>=1 yields this sequence.
MATHEMATICA
a[n_] := SeriesCoefficient[Product[k+x+(n-k+1)x^2, {k, 1, n}], {x, 0, n-1}];
Array[a, 23] (* Jean-François Alcover, Dec 29 2018 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 18 2018
STATUS
approved