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A221161 G.f.: Sum_{n>=0} (4*n+3)^n * x^n / (1 + (4*n+3)*x)^n. 8
1, 7, 72, 1056, 19968, 460800, 12533760, 392232960, 13872660480, 546979184640, 23781703680000, 1130106558873600, 58263271479705600, 3238634262940876800, 193064390900475494400, 12285915784575713280000, 831229959367865401344000, 59578968979556190388224000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = (2*n+5) * 4^(n-1) * n!  for n>0 with a(0)=1.

E.g.f.: (1 - x - 4*x^2) / (1-4*x)^2.

EXAMPLE

G.f.: A(x) = 1 + 7*x + 72*x^2 + 1056*x^3 + 19968*x^4 + 460800*x^5 +...

where

A(x) = 1 + 7*x/(1+7*x) + 11^2*x^2/(1+11*x)^2 + 15^3*x^3/(1+15*x)^3 + 19^4*x^4/(1+19*x)^4 + 23^5*x^5/(1+23*x)^5 +...

PROG

(PARI) {a(n)=polcoeff(sum(m=0, n, ((4*m+3)*x)^m/(1+(4*m+3)*x +x*O(x^n))^m), n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A187735, A014479, A187738, A187739, A221160, A187740.

Sequence in context: A230890 A203473 A197951 * A137730 A157920 A321077

Adjacent sequences:  A221158 A221159 A221160 * A221162 A221163 A221164

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 03 2013

STATUS

approved

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Last modified December 2 03:43 EST 2021. Contains 349437 sequences. (Running on oeis4.)