A262739 O.g.f. exp( Sum_{n >= 1} A262733(n)*x^n/n ).

1, 12, 215, 4564, 106442, 2635704, 68031147, 1810302340, 49308457334, 1368019979976, 38525145673126, 1098380420669000, 31641932951483220, 919622628946689648, 26931762975278938035, 793967020231145502564, 23543663463050594677310, 701763102761640853890600, 21014048069544552257072530, 631868353403527700756671320, 19070677448561228207945931276

Offset

0,2

Comments

O.g.f. is 1/x * the series reversion of x*(1 - x)^k/(1 + x)^(k+2) when k = 5. See the cross references for related sequences obtained from other values of k.

Links

Table of n, a(n) for n=0..20.

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

Formula

a(n-1) = 1/n * Sum_{i = 0..n-1} binomial(7*n,i)*binomial(6*n-i-2,n-i-1).

O.g.f.: A(x) = exp ( Sum_{n >= 1} 1/n! * (7*n)!/(7*n/2)! * (5*n/2)!/(5*n)!*x^n/n ) = 1 + 12*x + 215*x^2 + 4564*x^3 + ....

1 + x*A'(x)/A(x) is the o.g.f. for A262733.

O.g.f. is the series reversion of x*(1 - x)^5/(1 + x)^7,

a(0) = 1 and for n >= 1, a(n) = 1/n * Sum {k = 1..n} 1/k! * (7*k)!/(7*k/2)! * (5*k/2)!/(5*k)!*a(n-k).

Maple

A262739 := proc (n) option remember; if n = 0 then 1 else add(1/k!*(7*k)!/GAMMA(7*k/2 + 1)*GAMMA(5*k/2 + 1)/(5*k)!*A262739(n-k), k = 1 .. n)/n end if; end proc:
seq(A262739(n), n = 0..20);

Prog

(PARI) a(n) = sum(k=0, n, binomial(7*(n+1), k)*binomial(6*(n+1)-k-2, (n+1)-k-1))/(n+1); \\ Altug Alkan, Oct 03 2015

Crossrefs

Cf. A262733, A211419, A000108 (k = 0), A007297 (k = 1), A066357 (k = 2), A262737 (k = 3), A262738 (k = 4), A262740 (k = 6).

Sequence in context: A317199 A281253 A184711 * A027487 A276245 A241225

Adjacent sequences: A262736 A262737 A262738 * A262740 A262741 A262742

Keyword

nonn,easy

Author

Peter Bala, Sep 29 2015

Status

approved