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A126694 G.f.: 1/(1 - 7*x*c(x)), where c(x) is the g.f. for A000108. 8
1, 7, 56, 455, 3710, 30282, 247254, 2019087, 16488710, 134656130, 1099686056, 8980749862, 73342721956, 598965319960, 4891549246290, 39947649057855, 3262391226611830, 2664286127154330, 21758336553841440, 177693081299126610 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Hankel transform of this sequence is 7^n = [1, 7, 49, 343, 2401, ...] . The Hankel transform of the aerated sequence with g.f. 1/(1 - 7*x^2*c(x^2)) is also 7^n.

Numbers have the same parity as the Catalan numbers, that is, a(n) is even except for n of the form 2^m - 1. Follows from c(x) = 1/(1 - x*c(x)) == 1/(1 - 7*x*c(x)) (mod 2). - Peter Bala, Jul 24 2016

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(0) = 1, a(n) = (49*a(n-1) - 7*A000108(n-1))/6 for n >= 1.

a(n) = Sum_{k = 0..n} A106566(n,k)*7^k.

a(n) = Sum_{k = 0..n} A039599(n,k)*6^k.

CROSSREFS

Cf. A000108, A000984, A007854, A076035, A076036, A127628, A115970.

Sequence in context: A152776 A155197 A147839 * A305198 A264912 A024091

Adjacent sequences:  A126691 A126692 A126693 * A126695 A126696 A126697

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Feb 14 2007

STATUS

approved

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Last modified October 17 12:50 EDT 2018. Contains 316280 sequences. (Running on oeis4.)