A064308 -id:A064308 - cp's OEIS frontend

A064309 Row sums of triangle A064308.

1, 6, 38, 302, 2987, 35296, 481675, 7412010, 126421018, 2359544825, 47713420896, 1037071688566, 24072357120951, 593510886093458, 15472489081555834, 424833140882979666, 12244337906265312999, 369340369943742560692, 11629466311376482334088

Offset: 0

Wolfdieter Lang, Sep 13 2001

More terms from Sean A. Irvine, Jun 27 2023

A064307 Triangle of coefficients of certain numerator polynomials N(n,x).

Original entry on oeis.org

1, 1, 0, 1, 2, 1, 1, 10, 17, 2, 1, 37, 181, 111, 6, 1, 126, 1530, 2624, 741, 18, 1, 422, 11607, 43940, 34063, 4950, 57, 1, 1422, 83823, 616894, 1013799, 412698, 33337, 186, 1, 4853, 593203, 7846573, 23794925

Offset: 1

Wolfdieter Lang, Sep 13 2001

The g.f. for the sequence in the subdiagonal d>=1 (main diagonal: d=0) of triangle A064094 is N(d,x)/(1-x)^d.

Row sums give A001761(n+1). Main diagonal gives A000957(n+1), n >= 0.

			Triangle begins:
  1;
  1, 0;
  1, 2,  1;       N(3,x) = 1+2*x+x^2 = (1+x)^2.
  1, 10, 17,  2;
  1, 37, 181, 111, 6;
  ...

Cf. A000957, A001761, A064094.

a(n, m) = [x^m]N(n, x); N(n, x) = (1-x)^(n-1) + Sum_{k=1..n-1} A064308(n-1, k)*k!*x^k*(1-x)^(n-1-k) for n >= 2; N(1, x) = 1 = N(2, x).

cp's OEIS Frontend

A064309 Row sums of triangle A064308.

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A064307 Triangle of coefficients of certain numerator polynomials N(n,x).

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