A135852 A007318 * A103516 as a lower triangular matrix.

1, 3, 2, 8, 4, 3, 20, 6, 9, 4, 48, 8, 18, 16, 5, 112, 10, 30, 40, 25, 6, 256, 12, 45, 80, 75, 36, 7, 576, 14, 63, 140, 175, 126, 49, 8, 1280, 16, 84, 224, 350, 336, 196, 64, 9, 2816, 18, 108, 336, 630, 756, 588, 288, 81, 10

Offset

0,2

Comments

Binomial transform of triangle A103516.

Links

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

Formula

T(n, k) = (A007318 * A103516)(n, k).

T(n, 0) = A001792(n).

Sum_{k=0..n} T(n, k) = A099035(n+1).

T(n, k) = (k+1)*binomial(n, k), with T(n, 0) = (n+2)*2^(n-1), T(n, n) = n+1. - G. C. Greubel, Dec 07 2016

Example

First few rows of the triangle are:
    1;
    3,  2;
    8,  4,  3;
   20,  6,  9,  4;
   48,  8, 18, 16,  5;
  112, 10, 30, 40, 25,  6;
  256, 12, 45, 80, 75, 36,  7;
  ...

Mathematica

T[n_, k_]:= If[n==0, 1, If[k==0, (n+2)*2^(n-1), (k+1)*Binomial[n, k]]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Dec 07 2016 *)

Prog

(Sage)
def A135852(n, k):
    if (n==0): return 1
    elif (k==0): return (n+2)*2^(n-1)
    else: return (k+1)*binomial(n, k)
flatten([[A135852(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 07 2022

Crossrefs

Cf. A007318, A103516.

Cf. A001792 (1st column), A099035 (row sums).

Cf. A135853 (= A103516 * A007318).

Sequence in context: A344577 A019666 A110938 * A191731 A143515 A082333

Adjacent sequences: A135849 A135850 A135851 * A135853 A135854 A135855

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 01 2007

Extensions

Offset changed to 0 by G. C. Greubel, Feb 07 2022

Status

approved