A006669 Exponentiation of g.f. for Pell numbers.

0, 1, 2, 8, 32, 159, 882, 5475, 37256, 276004, 2207944, 18949677, 173475876, 1685805913, 17319275430, 187443865596, 2130493441472, 25360318907075, 315370749394134, 4088067189914051, 55128639891893220, 771992274220462744, 11207495397779852000

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(-1) = 1, a(n) = Sum_{k=0..n} binomial(n, k) * A000129(k) * a(n-k-1). - Sean A. Irvine, Jun 11 2017

Prog

(PARI) alias(A006669_vec, a6669); a6669=[]; A006669(n)={n<1&&return(-n); if(n>#a6669, a6669=concat(a6669, vector(n-#a6669)), a6669[n]&&return(a6669[n])); a6669[n]=sum(k=0, n, binomial(n, k)*A000129(k)*A006669(n-k-1))} \\ use e.g. A000129=n->imag((quadgen(8)+1)^n). - M. F. Hasler, Jun 15 2017

Crossrefs

Cf. A000129.

Sequence in context: A131785 A347363 A359398 * A193778 A030804 A319364

Adjacent sequences: A006666 A006667 A006668 * A006670 A006671 A006672

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved