A131824 Main diagonal of triangle A131823: a(n) = A131823(n,n) for n>=0.

1, 1, 2, 7, 24, 86, 316, 1177, 4424, 16744, 63724, 243618, 934870, 3598960, 13892776, 53756263, 208434024, 809658440, 3150218032, 12274694280, 47890456576, 187068828772, 731511810152, 2863308366462, 11217762520246, 43984983838966

Offset

0,3

Links

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

Formula

a(n) = [x^n] Product_{i=0..n-1} (1 + x^(2^i))^(n-i) for n>=0.

Maple

A131824 := proc(n) local f, i ; f := 1 ; if n = 1 then RETURN(1) ; fi ; for i from 0 to n-1 do f := taylor(f*(1+x^(2^i))^(n-i), x=0, n+1) ; od; coeftayl(f, x=0, n) ; end: seq(A131824(n), n=0..27) ; # R. J. Mathar, Jul 24 2007

Prog

(PARI) a(n)=if(n==0, 1, polcoeff(prod(i=0, n-1, (1 + x^(2^i) +x*O(x^n))^(n-i)), n))

Crossrefs

Cf. A131823.

Sequence in context: A141753 A014300 A128086 * A256938 A150389 A183876

Adjacent sequences: A131821 A131822 A131823 * A131825 A131826 A131827

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2007

Extensions

More terms from R. J. Mathar, Jul 24 2007

Status

approved