login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125027 Binomial transform of the "1,2,3..." triangle. 1
1, 3, 3, 9, 11, 6, 26, 32, 27, 10, 72, 86, 85, 54, 15, 192, 222, 233, 189, 95, 21, 496, 558, 597, 549, 371, 153, 28, 1248, 1374, 1473, 1446, 1160, 664, 231, 36, 3072, 3326, 3549, 3600, 3203, 2246, 1107, 332, 45, 7424, 7934, 8409, 8659, 8201, 6567, 4051, 1745, 459, 55, 17664, 18686 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..57.

FORMULA

Given the triangle (natural numbers in succession: 1; 2,3; 4,5,6;...) as an infinite matrix M and P = Pascal's triangle as a lower triangular matrix, perform P*M, deleting the zeros.

The row sums s(n) = 1, 6, 26, 95, 312, 952, ... obey (-3*n+2)*s(n) +(9*n+7)*s(n-1) +2*(-3*n-2)*s(n-2)=0. - R. J. Mathar, May 21 2018

EXAMPLE

First few rows of the triangle are:

1;

3, 3;

9, 11, 6;

26, 32, 27, 10;

72, 86, 85, 54, 15;

...

MAPLE

A27 := proc(n, k)

    option remember;

    if k>= 0 and k <=n then

        if k = 0 then

            1+procname(n-1, n-1) ;

        else

            procname(n, 0)+k ;

        end if;

    else

        0;

    end if;

end proc:

A125027 := proc(n, k)

    add( binomial(n, j)*A27(j, k), j=k..n) ;

end proc: # R. J. Mathar, May 21 2018

CROSSREFS

Cf. A072863 (first column), A000217 (diagonal), A164845 (subdiagonal).

Sequence in context: A121072 A133164 A022156 * A005296 A124281 A320293

Adjacent sequences:  A125024 A125025 A125026 * A125028 A125029 A125030

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Nov 15 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 10:39 EDT 2021. Contains 348160 sequences. (Running on oeis4.)