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.

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

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) # uses[PtransMatrix from 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