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A201953 A diagonal of irregular triangle A201949. 3
1, 3, 15, 90, 629, 5019, 45030, 448776, 4919321, 58825415, 762089899, 10633219662, 158974192987, 2535484008225, 42970371055268, 771162539117408, 14609924404202130, 291386317037291622, 6102681801481066642, 133910606028043519500, 3072216586896101950757 (list; graph; refs; listen; history; text; internal format)
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 A097188 A271930 * A185369 A024339 A319950

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

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Last modified July 15 00:36 EDT 2020. Contains 335762 sequences. (Running on oeis4.)