A201953 A diagonal of irregular triangle A201949.

1, 3, 15, 90, 629, 5019, 45030, 448776, 4919321, 58825415, 762089899, 10633219662, 158974192987, 2535484008225, 42970371055268, 771162539117408, 14609924404202130, 291386317037291622, 6102681801481066642, 133910606028043519500, 3072216586896101950757

Offset: 2

Author

Paul D. Hanna, Dec 06 2011

Keywords

• nonn

Comments

G.f. of row n in triangle A201949 equals Product_{k=0..n-1} (1 + k*x + x^2).

Examples

			E.g.f.: A(x) = x^2/2! + 3*x^3/3! + 15*x^4/4! + 90*x^5/5! + 629*x^6/6! + 5019*x^7/7! + 45030*x^8/8! + 448776*x^9/9! + 4919321*x^10/10! + ...
Triangle A201949 begins:
[1],
[1, 0, 1],
[(1), 1, 2, 1, 1],
[1,(3), 5, 6, 5, 3, 1],
[1, 6, (15), 24, 28, 24, 15, 6, 1],
[1, 10, 40, (90), 139, 160, 139, 90, 40, 10, 1],
[1, 15, 91, 300, (629), 945, 1078, 945, 629, 300, 91, 15, 1],  ...
where coefficients in parenthesis form the initial terms of this sequence.
		

Crossrefs

Cf. A201949, A201950, A201951, A201952.

Programs

PARI

{a(n) = polcoeff( prod(j=0, n-1, 1 + j*x + x^2), n-2)}
for(n=2,30,print1(a(n),", "))

Formula

E.g.f.: Sum_{n>=0} log(1 - x)^(2*n+2) / (n!*(n+2)!). - Paul D. Hanna, Feb 25 2019

a(n) = [x^(n-2)] Product_{k=0..n-1} (1 + k*x + x^2).

Extensions

Offset changed to 2 to agree with the e.g.f. - Paul D. Hanna, Feb 25 2019