login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A201952 A diagonal of irregular triangle A201949. 3
1, 1, 5, 24, 139, 945, 7377, 65016, 638418, 6910650, 81747665, 1049089470, 14516096009, 215419836359, 3412889885571, 57492203734320, 1026121982213480, 19342642266760680, 383995631680561234, 8007915240045479980, 175020604366224762038, 4000551483475536398178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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=1..22.

FORMULA

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

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

a(n) = (n-1)*a(n-1) + A201950(n-1) + A201953(n-1).

EXAMPLE

E.g.f.: A(x) = x + x^2/2! + 5*x^3/3! + 24*x^4/4! + 139*x^5/5! + 945*x^6/6! + 7377*x^7/7! + 65016*x^8/8! + 638418*x^9/9! + 6910650*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], ...

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-1)}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Cf. A201949, A201950, A201951, A201953.

Sequence in context: A256325 A286743 A232318 * A221788 A111766 A228067

Adjacent sequences:  A201949 A201950 A201951 * A201953 A201954 A201955

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 06 2011

EXTENSIONS

Offset changed to 1 to agree with the e.g.f. - Paul D. Hanna, Feb 25 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 30 22:57 EDT 2020. Contains 338095 sequences. (Running on oeis4.)