

A235936


Triangle of numerators of the unreduced coefficients of a numerical integration for a prediction Adams method.


0



1, 1, 1, 5, 8, 1, 9, 19, 5, 1, 251, 646, 264, 106, 19, 475, 1427, 798, 482, 173, 27, 19087, 65112, 46461, 37504, 20211, 6312, 863, 36799, 139849, 121797, 123133, 88547, 41499, 11351, 1375
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OFFSET

0,4


COMMENTS

The coefficients b(q,j) are such that:
(qj)!*j!*b(q,j) = (1)^(qj)*Int (from 0 to 1) u*(u1)*...*(uq) du/(uj).
0<=j<=q, 0<=q<=p where p is the degree (or order) of the numerical integration.
This is the first case of tridimensional b(i,q,j), the integration is from i to i+1, with i=0.
The b(q,j) are:
1;
1/2, 1/2;
5/12, 8/12, 1/12;
9/24, 19/24, 5/24, 1/24;
... etc.
The denominators are A232853(n).
The numerators are this sequence.
First column's numerators: A002657(n).
Main diagonal's numerators: (1)^(n+1)*A141417(n).
Row sums are: 1,2,12,24,... (A091137).


REFERENCES

P. Curtz, Intégration numérique des systèmes différentiels à conditions initiales, Note 12, Centre de Calcul Scientifique de l'Armement, Arcueil, (now DGA Maitrise de l'Information 35174 Bruz), 1969, see page 45.


LINKS

Table of n, a(n) for n=0..35.


FORMULA

Recurrence:
b(q,j) = (1)^(qj)*C(q,j)*b(q,q)+b(q1,j).
C(q,j)=q!/((qj)!*j!).


EXAMPLE

Triangle starts:
1;
1, 1;
5, 8, 1;
9, 19, 5, 1;
251, 646, 264, 106, 19;
...
Numerators of
b(0,0)=1, b(1,0)=(1/21)=1/2, b(1,1)=1/2, b(2,0)=(1/33/2+2)/2=5/12, b(2,1)=(1/31)=2/3=8/12, b(2,2)=(1/31/2)/2=1/12.


CROSSREFS

Sequence in context: A185393 A073333 A316229 * A260781 A306068 A021949
Adjacent sequences: A235933 A235934 A235935 * A235937 A235938 A235939


KEYWORD

tabl,frac,sign


AUTHOR

Paul Curtz, Jan 17 2014


STATUS

approved



