A064307 - OEIS

A064307

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

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

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OFFSET

1,5

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..41.

FORMULA

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

EXAMPLE

Triangle begins:

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;

...

CROSSREFS

Cf. A000957, A001761, A064094.

Sequence in context: A262226 A298158 A154989 * A165883 A370950 A260950

Adjacent sequences: A064304 A064305 A064306 * A064308 A064309 A064310

KEYWORD

nonn,tabl

AUTHOR

Wolfdieter Lang, Sep 13 2001

STATUS

approved