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A099038 Diagonal sums of a Krawtchouk triangle. 2
1, 1, 0, 1, 5, 6, 3, 13, 42, 55, 55, 162, 413, 591, 810, 2001, 4451, 6900, 11091, 24795, 51030, 84337, 147253, 309666, 610695, 1058041, 1928646, 3903175, 7528741, 13480380, 25126093, 49640405, 94739568, 173440389, 326974495, 636424008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Diagonal sums of A099037.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*Sum_{i=0..n} (-1)^i*C(k, i) * C(n-2k, k-i).

Conjecture: n*a(n) -n*a(n-1) +n*a(n-2) +3*(-n+1)*a(n-3) +(-5*n+13)*a(n-4) +(n-3)*a(n-5)=0. - R. J. Mathar, Dec 21 2014

MATHEMATICA

Table[Sum[Binomial[n - k, k]*Sum[(-1)^i*Binomial[k, i]*Binomial[n - 2*k, k - i], {i, 0, n}], {k, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, Dec 31 2017 *)

PROG

(PARI) for(n=0, 30, print1(sum(k=0, floor(n/2), binomial(n-k, k)*sum(i=0, n, (-1)^i*binomial(k, i)*binomial(n-2*k, k-i))), ", ")) \\ G. C. Greubel, Dec 31 2017

CROSSREFS

Cf. A077948.

Sequence in context: A153614 A195709 A257837 * A064206 A087197 A221216

Adjacent sequences:  A099035 A099036 A099037 * A099039 A099040 A099041

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 23 2004

STATUS

approved

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Last modified November 12 12:43 EST 2018. Contains 317109 sequences. (Running on oeis4.)