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

 

Logo

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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A268436 Triangle read by rows, T(n,k) = RF(n-k+1, n-k) * S1(n,k) where RF denotes the rising factorial and S1 the Stirling cycle numbers, for n>=0 and 0<=k<=n. 2
1, 0, 1, 0, 2, 1, 0, 24, 6, 1, 0, 720, 132, 12, 1, 0, 40320, 6000, 420, 20, 1, 0, 3628800, 460320, 27000, 1020, 30, 1, 0, 479001600, 53343360, 2728320, 88200, 2100, 42, 1, 0, 87178291200, 8693879040, 397111680, 11371920, 235200, 3864, 56, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

Peter Luschny, The P-transform.

FORMULA

T(n,k) = binomial(n,k)*Sum_{i=0..k} binomial(k,i)*A268438(n-k,i).

T(n,k) = binomial(-k,-n)*Sum_{i=0..n-k} binomial(-n,i)*A268437(n-k,i).

T(n,k) = 4^(n-k)*Gamma(n-k+1/2)*A132393(n,k)/sqrt(Pi).

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

T(n,n-1) = (n-1)*n for n>=1.

Recurrence: T(n,k) = 1 if k=n; 0 if k=0; and otherwise (n-1)*(4*(n-k)-2)*T(n-1,k) + T(n-1,k-1).

EXAMPLE

[1]

[0,         1]

[0,         2,        1]

[0,        24,        6,       1]

[0,       720,      132,      12,     1]

[0,     40320,     6000,     420,    20,    1]

[0,   3628800,   460320,   27000,  1020,   30,  1]

[0, 479001600, 53343360, 2728320, 88200, 2100, 42, 1]

MAPLE

T := (n, k) -> pochhammer(n-k+1, n-k)*abs(Stirling1(n, k)):

for n from 0 to 9 do seq(T(n, k), k=0..n) od;

# Alternatively:

T := proc(n, k) option remember;

  `if`( n=k, 1,

  `if`( k=0, 0,

   (n-1)*(4*(n-k)-2)*T(n-1, k)+T(n-1, k-1))) end:

for n from 0 to 7 do seq(T(n, k), k=0..n) od;

MATHEMATICA

T[n_, k_] := Pochhammer[n-k+1, n-k] Abs[StirlingS1[n, k]];

Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 12 2019 *)

PROG

(Sage)

A268436 = lambda n, k: rising_factorial(n-k+1, n-k)*stirling_number1(n, k)

[[A268436(n, k) for k in (0..n)] for n in range(8)]

CROSSREFS

Cf. A132393, A268435, A268437, A268438.

Sequence in context: A269946 A009829 A202697 * A249570 A051652 A077019

Adjacent sequences:  A268433 A268434 A268435 * A268437 A268438 A268439

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Mar 07 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 December 1 11:30 EST 2021. Contains 349429 sequences. (Running on oeis4.)