A262738 O.g.f. exp( Sum_{n >= 1} A211419(n)*x^n/n ).

1, 10, 149, 2630, 51002, 1050132, 22539085, 498732014, 11296141454, 260613866380, 6103074997890, 144696786555580, 3466352150674324, 83776927644646952, 2040261954214847421, 50018542073019175806, 1233419779839067305350, 30572886836581693309020

Offset: 0

Author

Peter Bala, Sep 29 2015

Keywords

• nonn
• easy

Comments

O.g.f. is 1/x * the series reversion of x*(1 - x)^k/(1 + x)^(k+2) at k = 4. See the cross references for related sequences obtained from other values of k.

Links

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

Crossrefs

Cf. A211419, A000108 (k = 0), A007297 (k = 1), A066357 (k = 2), A262737 (k = 3), A262739 (k = 5), A262740 (k = 6).

Programs

Maple

A262738 := proc(n) option remember; if n = 0 then 1 else add((6*k)!*(2*k)!/((4*k)!*(3*k)!*k!)*A262738(n-k), k = 1 .. n)/n end if; end proc:
seq(A262738(n), n = 0..20);

PARI

a(n) = sum(k=0, n, binomial(6*(n+1),k)*binomial(5*(n+1)-k-2,(n+1)-k-1))/(n+1); \\ Altug Alkan, Oct 03 2015

Formula

a(n-1) = 1/n * Sum_{i = 0..n-1} binomial(6*n,i)*binomial(5*n-i-2,n-i-1).

O.g.f.: A(x) = exp ( Sum_{n >= 1} (6*n)!*(2*n)!/((4*n)!*(3*n)!*n!)*x^n/n ) = 1 + 10*x + 149*x^2 + 2630*x^3 + ....

1 + x*A'(x)/A(x) is the o.g.f. for A211419.

O.g.f. is the series reversion of x*(1 - x)^4/(1 + x)^6.

a(0) = 1 and for n >= 1, a(n) = 1/n * Sum {k = 1..n} (6*k)!*(2*k)!/((4*k)!*(3*k)!*k!)*a(n-k).