A087736 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A087736

Triangle T(n,k) read by rows given by [0, 1, 3, 6, 10, 15, 21, ...] DELTA [1, 3, 6, 10, 15, 21, 28,...] where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 4, 0, 4, 23, 34, 0, 34, 249, 606, 496, 0, 496, 4354, 14181, 20434, 11056, 0, 11056, 112238, 450097, 894838, 885032, 349504, 0, 349504, 4008024, 18911670, 47136095, 65613780, 48468804, 14873104

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,6

LINKS

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

FORMULA

Sum_{k, 0<=k<=n}T(n,k)*x^(n-k)=A000012(n), A011782(n), A001147(n), A002105(n+1), A000364(n), A126151(n), A126156(n) for n = -3,-2,-1,0,1,2,3 respectively .

EXAMPLE

Triangle begins:

0, 1;

0, 1, 4;

0, 4, 23, 34;

0, 34, 249, 606, 496;

0, 496, 4354, 14181, 20434, 11056;

0, 11056, 112238, 450097, 894838, 885032, 349504;

0, 349504, 4008024, 18911670, 47136095, 65613780, 48468804, 14873104 ;...

CROSSREFS

Diagonals give A002105: [1, 1, 4, 34, 496, ...] Row sums give A000364 : [1, 1, 5, 61, 1385, ...] Euler numbers.

Cf. A000217 A000384 A002105 A084938.

Sequence in context: A151672 A058493 A112149 * A005075 A103638 A129821

Adjacent sequences: A087733 A087734 A087735 * A087737 A087738 A087739

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Sep 30 2003, Jul 17 2007

EXTENSIONS

Corrected and edited. - Philippe Deléham, Nov 24 2008

STATUS

approved