A137638 Antidiagonal sums of square array A137634.

1, 3, 15, 72, 361, 1840, 9505, 49578, 260540, 1377328, 7316373, 39020372, 208809544, 1120621368, 6029023185, 32507001876, 175604614108, 950233307930, 5149691511432, 27946158749572, 151843410356906, 825949622559366

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: A(x) = 2*(1+x)/((1+2*x + G(x))*G(x)) where G(x) = sqrt(1 - 4*x*(1+x)^2).

a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n-k+2*j,j)*C(n-k+2*j,k-j).

D-finite with recurrence 2*(n+1)*a(n) +(-3*n-7)*a(n-1) +2*(-17*n+10)*a(n-2) +8*(-7*n+10)*a(n-3) +2*(-18*n+37)*a(n-4) +4*(-2*n+5)*a(n-5)=0. - R. J. Mathar, Jun 23 2023

Prog

(PARI) {a(n)=sum(k=0, n, sum(j=0, k, binomial(2*j+n-k, j)*binomial(2*j+n-k, k-j)))} /* Using the g.f.: */ {a(n)=local(G=sqrt(1 - 4*x*(1+x)^2 +x*O(x^n))); polcoeff(2*(1+x)/((1+2*x+G)*G), n)}

Crossrefs

Cf. A137634, A137635, A137636, A137637.

Sequence in context: A357161 A290902 A155117 * A156019 A145839 A232289

Adjacent sequences: A137635 A137636 A137637 * A137639 A137640 A137641

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2008

Status

approved