A316595 a(n) equals the coefficient of x^n in Sum_{m>=0} (x^m + 5 + 1/x^m)^m for n >= 1.

1, 10, 78, 561, 3885, 26565, 180285, 1221554, 8272252, 56063900, 380361212, 2583878630, 17575724491, 119705606020, 816297170565, 5572946307857, 38088275031435, 260576838539320, 1784382167211378, 12229792806897910, 83888652677221112, 575858960208964685, 3955813057814040153, 27192049709537787123, 187032147327469550926, 1287187641890879422980, 8863461073824746853534, 61064188079233277265138, 420899733623010047381885, 2902469328540659624278455

Offset

1,2

Comments

The coefficient of 1/x^n in Sum_{m>=0} (x^m + 5 + 1/x^m)^m equals a(n) for n > 0, while the constant term in the sum increases without limit.

a(n) = Sum_{k=0..n-1} A316590(n,k) * 5^k for n >= 1.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..260

Formula

a(n) ~ 7^(n + 1/2) / (2*sqrt(Pi*n)). - Vaclav Kotesovec, Jul 10 2018

Example

G.f.: A(x) = x + 10*x^2 + 78*x^3 + 561*x^4 + 3885*x^5 + 26565*x^6 + 180285*x^7 + 1221554*x^8 + 8272252*x^9 + 56063900*x^10 + ...
such that Sum_{m>=0} (x^m + 5 + 1/x^m)^m = A(x) + A(1/x) + (infinity)*x^0.

Prog

(PARI) {a(n) = polcoeff( sum(m=1, n, (x^-m + 5 + x^m)^m +x*O(x^n)), n, x)}
for(n=1, 40, print1(a(n), ", "))

Crossrefs

Cf. A304638, A316590, A316591, A316592, A316593, A316594.

Sequence in context: A298270 A082136 A153596 * A348314 A056986 A243247

Adjacent sequences: A316592 A316593 A316594 * A316596 A316597 A316598

Keyword

nonn

Author

Paul D. Hanna, Jul 08 2018

Status

approved