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

2,2

Comments

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

Links

Table of n, a(n) for n=2..22.

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).

Example

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.

Prog

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

Crossrefs

Cf. A201949, A201950, A201951, A201952.

Sequence in context: A025748 A366085 A271930 * A355501 A185369 A024339

Adjacent sequences: A201950 A201951 A201952 * A201954 A201955 A201956

Keyword

nonn

Author

Paul D. Hanna, Dec 06 2011

Extensions

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

Status

approved