A262015 - OEIS

A262015

a(n) = [x^n] (1-x)^(4*n+1) * Sum_{k>=0} binomial(n+k-1,k)^4 * x^k.

1, 11, 603, 49682, 4961755, 554083761, 66555527346, 8415759917268, 1105492743188955, 149552158117961225, 20710288432292240353, 2923132560874617706758, 419153950726771517250994, 60909593781491823719018822, 8952489587089165075007703060, 1328855554150146863702291235432, 198950469430034588049648664728027, 30012345078088728771497844274527081

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OFFSET

0,2

LINKS

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

Peter Bala, A recurrence for A262015.

FORMULA

From Peter Bala, Sep 21 2025: (Start)

a(n) = Sum_{k = 0..n} (-1)^(n-k)*binomial(n+k, k)^4*binomial(4*n+1, n-k).

a(n) = binomial(-3*n-2, n)*hypergeom([n+1, n+1, n+1, n+1, -n], [1, 1, 1, 3*n+2], 1). (End)

MAPLE

seq(simplify(binomial(-3*n-2, n)*hypergeom([n+1, n+1, n+1, n+1, -n], [1, 1, 1, 3*n+2], 1)), n = 0..20); # Peter Bala, Sep 21 2025