A371486 G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1-x))^4.

1, 4, 30, 260, 2465, 24796, 260008, 2811216, 31117240, 350890260, 4016744586, 46556054072, 545273713228, 6443442857024, 76727957438650, 919796418086076, 11091249210406816, 134439965189940176, 1637160457090585016, 20019920157735604796, 245733987135102838131

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} binomial(n-1,n-k) * binomial(5*k+3,k)/(k+1).

G.f.: A(x) = B(x/(1-x)), where B(x) = (1/x) * Series_Reversion( x*(1-x)^4 ).

G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A349332.

Prog

(PARI) a(n) = sum(k=0, n, binomial(n-1, n-k)*binomial(5*k+3, k)/(k+1));

Crossrefs

Cf. A002212, A270386, A371483.

Cf. A118971, A349332.

Sequence in context: A201200 A102307 A209441 * A352863 A330801 A052658

Adjacent sequences: A371483 A371484 A371485 * A371487 A371488 A371489

Keyword

nonn

Author

Seiichi Manyama, Mar 25 2024

Status

approved