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A064307 Triangle of coefficients of certain numerator polynomials N(n,x). 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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

CROSSREFS

Sequence in context: A153731 A262226 A154989 * A165883 A260950 A110905

Adjacent sequences:  A064304 A064305 A064306 * A064308 A064309 A064310

KEYWORD

nonn,tabl

AUTHOR

Wolfdieter Lang, Sep 13 2001

STATUS

approved

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Last modified December 14 00:21 EST 2017. Contains 295976 sequences.