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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269943 Triangle read by rows, T(n,k) = ((-1)^k*(2*n)!/4^k)*P[n,k](1/((2*n-1)*(2*n))) where P is the inverse P-transform, for n>=0 and 0<=k<=n. 0
1, 0, 1, 0, 2, 6, 0, 16, 60, 90, 0, 288, 1176, 2520, 2520, 0, 9216, 39360, 98280, 151200, 113400, 0, 460800, 2023296, 5504400, 10311840, 12474000, 7484400, 0, 33177600, 148442112, 426666240, 896575680, 1362160800, 1362160800, 681080400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The P-transform is defined in the link. Compare also the Sage implementation below.

LINKS

Table of n, a(n) for n=0..35.

Peter Luschny, The P-transform.

FORMULA

T(n,1) = 2^(n-1)*(n-1)!^2 (cf. A055546) for n>=1.

T(n,n) = (2*n)!/2^n = A000680(n).

EXAMPLE

Triangle starts:

[1]

[0, 1]

[0, 2, 6]

[0, 16, 60, 90]

[0, 288, 1176, 2520, 2520]

[0, 9216, 39360, 98280, 151200, 113400]

[0, 460800, 2023296, 5504400, 10311840, 12474000, 7484400]

PROG

(Sage)

# The function PtransMatrix is defined in A269941:

eul = lambda n: 1/((2*n-1)*(2*n))

norm = lambda n, k: (-1)^k*factorial(2*n)/4^k

PtransMatrix(7, eul, norm, inverse = True)

CROSSREFS

Cf. A000680, A055546.

Sequence in context: A131105 A321713 A057635 * A243015 A139717 A285119

Adjacent sequences:  A269940 A269941 A269942 * A269944 A269945 A269946

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Mar 27 2016

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 January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)