A322627 a(n) = [y^(n+1)] (n + y) * Product_{k=1..2*n} (k + y), for n >= 0.

1, 4, 55, 1260, 40593, 1690920, 86550035, 5260335080, 370410456273, 29664913887180, 2663386839535695, 265000164136279572, 28945346029081686865, 3443628513369917505360, 443271719760096505911675, 61385459345641259759898000, 9100387546322497725789848865, 1438068852777042379374392377620, 241308826278118770656171323634855, 42852242077203438281471161279058300

Offset: 0

Author

Paul D. Hanna, Jan 26 2019

Keywords

• nonn

Comments

A diagonal in triangle A268647: a(n) = A268647(n, n+1) for n >= 0.

Examples

			The coefficients of y^k in (n + y) * Product_{j=1..2*n} (j + y), for k=0..2*n+1, yields row n of triangle A268647, which begins:
0, 1;
2, 5, 4, 1;
48, 124, 120, 55, 12, 1;
2160, 6012, 6636, 3829, 1260, 238, 24, 1;
161280, 478656, 582080, 387260, 157080, 40593, 6720, 690, 40, 1;
18144000, 56772000, 74396520, 54801076, 25494150, 7927205, 1690920, 248523, 24750, 1595, 60, 1; ...
this sequence is the diagonal a(n) = A268647(n, n+1) for n >= 0.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A268647.

Programs

PARI

/* a(n) = [y^(n+1)] (n + y)*Product_{k=1..2*n} (k + y) */
{A268647(n, k) = polcoeff((n + y)*prod(k=1, 2*n, k + y), k, y)}
{a(n) = A268647(n, n+1)}
for(n=0, 25,  print1(a(n),", "));