login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101516 Antidiagonal sums of symmetric square array A101515 and also equals the binomial transform of a sequence formed from terms of A101514 repeated twice. 2
1, 2, 4, 8, 17, 38, 91, 232, 632, 1824, 5571, 17892, 60355, 212898, 784416, 3008480, 11997341, 49612426, 212536067, 941213428, 4305049140, 20302469824, 98641434683, 493038167880, 2533414749409, 13366134856170, 72361098996208 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A101514 equals the main diagonal of A101515 shift one place right and also A101514 shifts one place left under the square binomial transform (A008459): A101514(n+1) = Sum_{k=0..n-1} C(n-1,k)^2*A101514(k).

LINKS

Table of n, a(n) for n=0..26.

FORMULA

G.f.: A(x) = G101514(x^2/(1-x)^2)/(1-x)^2, where G101514(x)= g.f. of A101514. a(n) = Sum_{k=0..n} C(n, k)*A101514([k/2]).

EXAMPLE

Given A101514 = [1,1,2,7,35,236,2037,21695,277966,4198635,...],

the binomial transform of A101514 terms repeated twice returns this sequence:

BINOMIAL[1,1,1,1,2,2,7,7,35,35,...] = [1,2,4,8,17,38,91,232,632,1824,...].

PROG

(PARI) {a(n)=sum(k=0, n, binomial(n, k)* if(k\2==0, 1, sum(j=0, k\2-1, binomial(k\2-1, j)^2* sum(i=0, 2*j, (-1)^(2*j-i)*binomial(2*j, i)*a(i)))))}

CROSSREFS

Cf. A101514, A101515.

Sequence in context: A086615 A081124 A090901 * A118928 A049312 A132043

Adjacent sequences:  A101513 A101514 A101515 * A101517 A101518 A101519

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 06 2004

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 00:03 EST 2018. Contains 299472 sequences. (Running on oeis4.)