A134417 Triangle read by rows: T(n,k) = binomial(n,k)*A133632(k + 1).

1, 1, 4, 1, 8, 5, 1, 12, 15, 20, 1, 16, 30, 80, 25, 1, 20, 50, 200, 125, 100, 1, 24, 75, 400, 375, 600, 125, 1, 28, 105, 700, 875, 2100, 875, 500, 1, 32, 140, 1120, 1750, 5600, 3500, 4000, 625, 1, 36, 180, 1680, 3150, 12600, 10500, 18000, 5625, 2500

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Formula

G.f.: (1 - (1 - 4*y)*x)/(1 - 2*x + (1 - 5*y^2)*x^2). - Andrew Howroyd, Sep 21 2025

Example

First few rows of the triangle:
  1;
  1,  4;
  1,  8,  5;
  1, 12, 15,  20;
  1, 16, 30,  80,  25;
  1, 20, 50,  20, 125, 100;
  1, 24, 75, 400, 375, 600, 125;
  ...

Prog

(PARI) T(n) = [Vecrev(p) | p<-Vec((1 - (1 - 4*y)*x)/(1 - 2*x + (1 -5*y^2)*x^2) + O(x*x^n))]
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Sep 21 2025

Crossrefs

Row sums are A134418.

Main diagonal is A133632(n+1).

Sequence in context: A193337 A141567 A254707 * A116080 A343125 A205296

Adjacent sequences: A134414 A134415 A134416 * A134418 A134419 A134420

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 24 2007

Extensions

New name and offset changed by Andrew Howroyd, Sep 21 2025

Status

approved