A108478 Diagonal sums of number triangle A108477.

1, 1, 2, 14, 43, 127, 468, 1596, 5253, 17917, 60918, 205194, 694287, 2351611, 7951336, 26894840, 91004105, 307854073, 1041410602, 3523170438, 11918842803, 40320750711, 136404504124, 461454010164, 1561085306061, 5281113937653

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

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

Empirical g.f.: -(3*x^3+x^2+x-1) / ((x^3-3*x^2-x-1)*(x^3+x^2+3*x-1)). - Colin Barker, Sep 26 2014

Maple

A108478:=n->add(add(binomial(2*(n-2*k), j)*binomial(2*k, j)*2^j, j=0..n-k), k=0..floor(n/2)): seq(A108478(n), n=0..30); # Wesley Ivan Hurt, Sep 26 2014

Mathematica

Table[Sum[Sum[Binomial[2 (n - 2 k), j]*Binomial[2 k, j]*2^j, {j, 0, n - k}], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Wesley Ivan Hurt, Sep 26 2014 *)

Prog

(PARI) a(n) = sum(k=0, n\2, sum(j=0, n-k, binomial(2*(n-2*k), j)*binomial(2*k, j)*2^j)); \\ Michel Marcus, Sep 26 2014

Crossrefs

Sequence in context: A192375 A267247 A297425 * A262963 A195960 A268684

Adjacent sequences: A108475 A108476 A108477 * A108479 A108480 A108481

Keyword

easy,nonn

Author

Paul Barry, Jun 04 2005

Status

approved