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A108478 Diagonal sums of number triangle A108477. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)