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!)
A115991 Number triangle T(n,k) = Sum_{j=0..n} C(n-k,j-k)*C(j,n-j)*2^(n-j). 2
1, 1, 1, 5, 3, 1, 13, 9, 5, 1, 49, 31, 17, 7, 1, 161, 105, 61, 29, 9, 1, 581, 371, 217, 111, 45, 11, 1, 2045, 1313, 781, 417, 189, 65, 13, 1, 7393, 4719, 2825, 1551, 753, 303, 89, 15, 1, 26689, 17041, 10277, 5757, 2921, 1289, 461, 117, 17, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

First column is A084601 with e.g.f. exp(x) Bessel_I(0,2sqrt(2)x). Row sums are A098518(n+1) with e.g.f. dif(exp(x) Bessel_I(1,2sqrt(2)x)/sqrt(2)).

Riordan array (1/sqrt(1-2*x-7*x^2), (1+x-sqrt(1-2*x-7*x^2))/2).

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

EXAMPLE

Triangle begins as:

    1;

    1,   1;

    5,   3,   1;

   13,   9,   5,   1;

   49,  31,  17,   7,  1;

  161, 105,  61,  29,  9,  1;

  581, 371, 217, 111, 45, 11, 1;

MATHEMATICA

Table[Sum[Binomial[n-k, j-k]*Binomial[j, n-j]*2^(n-j), {j, 0, n}], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, May 09 2019 *)

PROG

(PARI) {T(n, k) = sum(j=0, n, binomial(n-k, j-k)*binomial(j, n-j)*2^(n-j))}; \\ G. C. Greubel, May 09 2019

(MAGMA) [[(&+[Binomial(n-k, j-k)*Binomial(j, n-j)*2^(n-j): j in [0..n]]): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 09 2019

(Sage) [[sum(binomial(n-k, j-k)*binomial(j, n-j)*2^(n-j) for j in (0..n)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, May 09 2019

(GAP) Flat(List([0..10], n-> List([0..n], k-> Sum([0..n], j-> Binomial(n-k, j-k)*Binomial(j, n-j)*2^(n-j)) ))); # G. C. Greubel, May 09 2019

CROSSREFS

Cf. A084601, A098518.

Sequence in context: A229958 A157891 A173644 * A143410 A114344 A317674

Adjacent sequences:  A115988 A115989 A115990 * A115992 A115993 A115994

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Feb 10 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 February 16 21:37 EST 2020. Contains 331975 sequences. (Running on oeis4.)