A152601 a(n) = Sum_{k=0..n} C(n+k,2k)*A000108(k)*3^k*2^(n-k).

1, 5, 40, 395, 4360, 51530, 637840, 8163095, 107140360, 1434252230, 19507077040, 268796321870, 3744480010960, 52647783144980, 746145741252640, 10648007952942095, 152877753577617160, 2206713692628578030

Offset

0,2

Comments

Hankel transform is 15^C(n+1,2).

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = A152600(n+1)/2.

a(n) = Sum_{k=0..n} A088617(n,k)*3^k*2^(n-k) = Sum_{k=0..n} A060693(n,k)*2^k*3^(n-k). - Philippe Deléham, Dec 10 2008

a(n) = Sum_{k=0..n} A090181(n,k)*5^k*3^(n-k). - Philippe Deléham, Dec 10 2008

a(n) = Sum_{k=0..n} A131198(n,k)*3^k*5^(n-k). - Philippe Deléham, Dec 10 2008

a(n) = Sum_{k=0..n} A133336(n,k)*(-2)^k*5^(n-k) = Sum_{k=0..n} A086810(n,k)*5^k*(-2)^(n-k). - Philippe Deléham, Dec 10 2008

G.f.: 1/(1-5x/(1-3x/(1-5x/(1-3x/(1-5x/(1-3x/(1-5x/(1-... (continued fraction). - Philippe Deléham, Nov 28 2011

Conjecture: (n+1)*a(n) +8*(-2*n+1)*a(n-1) +4*(n-2)*a(n-2)=0. - R. J. Mathar, Nov 24 2012

G.f.: 1/G(x), with G(x) = 1-2*x-(3*x)/G(x) (continued fraction). - Nikolaos Pantelidis, Jan 09 2023

Crossrefs

Cf. A103211, A103210.

Cf. A088617, A060693, A090181, A131198, A133336, A086810

Cf. A152600.

Sequence in context: A130564 A368011 A124555 * A079158 A061633 A371372

Adjacent sequences: A152598 A152599 A152600 * A152602 A152603 A152604

Keyword

easy,nonn

Author

Paul Barry, Dec 09 2008

Status

approved