A262740 O.g.f. exp( Sum_{n >= 1} A211421(n)*x^n/n ).

1, 14, 293, 7266, 197962, 5726364, 172662765, 5367187226, 170772853790, 5534640052292, 182070248073826, 6063785526898644, 204055962203476788, 6927718839334775608, 236994877398511998717, 8161492483543100398410, 282705062046649346154006, 9843330120848835962213940

Offset

0,2

Comments

O.g.f. is 1/x * the series reversion of x*(1 - x)^k/(1 + x)^(k+2) at k = 6. See the cross references for related sequences obtained from other values of k.

Links

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

Peter Bala, Notes on logarithmic differentiation, the binomial transform and series reversion

Formula

a(n-1) = 1/n * Sum_{i = 0..n-1} binomial(8*n,i)*binomial(7*n-i-2,n-i-1).

O.g.f.: A(x) = exp ( Sum_{n >= 1} 1/n! * (8*n)!/(4*n)! * (3*n)!/(6*n)!*x^n/n ) = 1 + 14*x + 293*x^2 + 7266*x^3 + ....

1 + x*A'(x)/A(x) is the o.g.f. for A211421.

O.g.f. is the series reversion of x*(1 - x)^6/(1 + x)^8.

a(0) = 1 and for n >= 1, a(n) = 1/n * Sum {k = 1..n} 1/k! * (8*k)!/(4*k)! * (3*k)!/(6*k)!*a(n-k).

Maple

#A262740
A262740 := proc (n) option remember; if n = 0 then 1 else add(1/k!*(8*k)!/(4*k)!*(3*k)!/(6*k)!*A262740(n-k), k = 1 .. n)/n end if; end proc:
seq(A262740(n), n = 0..17);

Prog

(PARI) a(n) = sum(k=0, n, binomial(8*(n+1), k)*binomial(7*(n+1)-k-2, (n+1)-k-1))/(n+1); \\ Altug Alkan, Oct 03 2015

Crossrefs

Cf. A211421, A000108 (k = 0), A007297 (k = 1), A066357 (k = 2), A262737 (k = 3), A262738 (k = 4), A262739 (k = 5).

Sequence in context: A181192 A227580 A215869 * A158475 A116165 A186376

Adjacent sequences: A262737 A262738 A262739 * A262741 A262742 A262743

Keyword

nonn,easy

Author

Peter Bala, Sep 29 2015

Status

approved