A254633 -id:A254633

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

Search: a254633 -id:a254633

Displaying 1-1 of 1 result found.

page 1

A254632

Triangle read by rows, T(n, k) = 4^n*[x^k]hypergeometric([3/2, -n], [3], -x), n>=0, 0<=k<=n.

+10
3

1, 4, 2, 16, 16, 5, 64, 96, 60, 14, 256, 512, 480, 224, 42, 1024, 2560, 3200, 2240, 840, 132, 4096, 12288, 19200, 17920, 10080, 3168, 429, 16384, 57344, 107520, 125440, 94080, 44352, 12012, 1430, 65536, 262144, 573440, 802816, 752640, 473088, 192192, 45760, 4862

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..44.

FORMULA

T(n,0) = A000302(n).

T(n,n) = A000108(n+1).

T(n,1) = A002699(n) for n>=1.

T(n,n-1) = A128650(n+2) for n>=1.

T(2*n,n) = A254633(n).

T(n,k) = 4^(n-k)*C(n,k)*Catalan(k+1).

sum(k=0..n, T(n,k)) = A025230(n+2).

EXAMPLE

[ 1]

[ 4, 2]

[ 16, 16, 5]

[ 64, 96, 60, 14]

[ 256, 512, 480, 224, 42]

[1024, 2560, 3200, 2240, 840, 132]

[4096, 12288, 19200, 17920, 10080, 3168, 429]

MAPLE

h := n -> simplify(hypergeom([3/2, -n], [3], -x)):

seq(print(seq(4^n*coeff(h(n), x, k), k=0..n)), n=0..9);

MATHEMATICA

T[n_, k_] := 4^(n-k) Binomial[n, k] CatalanNumber[k+1];

Table[T[n, k], {n, 0, 8}, {k, 0, n}] (* Jean-François Alcover, Jun 28 2019 *)

PROG

(Sage)

A254632 = lambda n, k: (4)^(n-k)*binomial(n, k)*catalan_number(k+1)

for n in range(7): [A254632(n, k) for k in (0..n)]

CROSSREFS

Cf. A108198 (Peter Bala), A000302, A000108, A025230, A002699, A128650, A254633.

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Feb 03 2015

STATUS

approved

page 1

Search completed in 0.005 seconds