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!)
A158785 Expansion of e.g.f.: exp(t*x)/(1 - x^2/t - t^3*x^3). 1
1, 0, 1, 2, 0, 0, 1, 0, 6, 0, 0, 7, 24, 0, 0, 12, 0, 0, 25, 0, 120, 0, 0, 260, 0, 0, 61, 720, 0, 0, 360, 0, 0, 1470, 0, 0, 841, 0, 5040, 0, 0, 15960, 0, 0, 5082, 0, 0, 5251, 40320, 0, 0, 20160, 0, 0, 122640, 0, 0, 134456, 0, 0, 20497, 0, 362880, 0, 0, 1512000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Rows n = 0..50 of the irregular triangle, flattened

FORMULA

T(n, k) = coefficients of e.g.f.: t^floor(n/2)*exp(t*x)/(1 - x^2/t - t^3*x^3).

From G. C. Greubel, Dec 05 2021: (Start)

T(n, floor(n/2) + n) = A330044(n).

T(n, 0) = A005359(n).

T(n, 1) = A005212(n). (End)

EXAMPLE

Irregular triangle begins as:

      1;

      0,    1;

      2,    0, 0,     1;

      0,    6, 0,     0,     7;

     24,    0, 0,    12,     0, 0,     25;

      0,  120, 0,     0,   260, 0,      0,   61;

    720,    0, 0,   360,     0, 0,   1470,    0, 0,    841;

      0, 5040, 0,     0, 15960, 0,      0, 5082, 0,      0, 5251;

  40320,    0, 0, 20160,     0, 0, 122640,    0, 0, 134456,    0, 0, 20497;

MATHEMATICA

Table[CoefficientList[Expand[t^Floor[n/2]*n!*SeriesCoefficient[Series[Exp[t*x]/(1 - x^2/t - t^3*x^3), {x, 0, 20}], n]], t], {n, 0, 10}]//Flatten

PROG

(Sage)

f(x, t) = exp(t*x)/(1 - x^2/t - t^3*x^3)

def A158785(n, k): return ( factorial(n)*t^(n//2)*( f(x, t) ).series(x, 20).list()[n] ).series(t, 2*n+1).list()[k]

flatten([[A158785(n, k) for k in (0..n+(n//2))] for n in (0..10)]) # G. C. Greubel, Dec 05 2021

CROSSREFS

Cf. A005212, A005359, A158706, A158757, A330044.

Sequence in context: A347097 A339274 A335156 * A346243 A349916 A349342

Adjacent sequences:  A158782 A158783 A158784 * A158786 A158787 A158788

KEYWORD

nonn,tabl,changed

AUTHOR

Roger L. Bagula, Mar 26 2009

EXTENSIONS

Edited by G. C. Greubel, Dec 05 2021

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 9 07:53 EST 2021. Contains 349627 sequences. (Running on oeis4.)