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A176334 Diagonal sums of number triangle A176331. 3
1, 1, 2, 4, 9, 21, 51, 124, 305, 755, 1879, 4698, 11792, 29694, 74984, 189811, 481498, 1223713, 3115200, 7942134, 20275362, 51823246, 132604193, 339644739, 870745187, 2234208932, 5737129623, 14742751524, 37909928908, 97543380598 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

MAPLE

A176334 := proc(n)

    add(add(binomial(j, n-2*k)*binomial(j, k)*(-1)^(n-k-j), j=0..n-k), k=0..floor(n/2)) ;

end proc: # R. J. Mathar, Feb 10 2015

MATHEMATICA

T[n_, k_]:= T[n, k]= Sum[(-1)^(n-j)*Binomial[j, k]*Binomial[j, n-k], {j, 0, n}]; Table[Sum[T[n-k, k], {k, 0, Floor[n/2]}], {n, 0, 30}] (* G. C. Greubel, Dec 07 2019 *)

PROG

(PARI) T(n, k) = sum(j=0, n, (-1)^(n-j)*binomial(j, n-k)*binomial(j, k));

vector(30, n, sum(j=0, (n-1)\2, T(n-j-1, j)) ) \\ G. C. Greubel, Dec 07 2019

(MAGMA) T:= func< n, k | &+[(-1)^(n-j)*Binomial(j, n-k)*Binomial(j, k): j in [0..n]] >;

[(&+[T(n-k, k): k in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, Dec 07 2019

(Sage)

@CachedFunction

def T(n, k): return sum( (-1)^(n-j)*binomial(j, n-k)*binomial(j, k) for j in (0..n))

[sum(T(n-k, k) for k in (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Dec 07 2019

(GAP)

T:= function(n, k)

    return Sum([0..n], j-> (-1)^(n-j)*Binomial(j, k)*Binomial(j, n-k) );

  end;

List([0..30], n-> Sum([0..Int(n/2)], j-> T(n-j, j) )); # G. C. Greubel, Dec 07 2019

CROSSREFS

Cf. A176331, A176332, A176335.

Sequence in context: A199410 A091600 A261232 * A257386 A048285 A051529

Adjacent sequences:  A176331 A176332 A176333 * A176335 A176336 A176337

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 15 2010

STATUS

approved

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Last modified May 16 22:18 EDT 2021. Contains 343957 sequences. (Running on oeis4.)