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A246572 G.f.: sqrt( Sum_{n>=0} x^n / (1-x)^(4*n+1) * [Sum_{k=0..2*n} C(2*n,k)^2 * x^k]^2 ). 4
1, 1, 7, 51, 425, 3879, 36527, 355333, 3531175, 35673875, 365179885, 3777991337, 39430009247, 414567124053, 4386228722281, 46659584847835, 498701253293129, 5352318710976505, 57655365854918487, 623105208980304843, 6753999316026236871, 73403038257774972101, 799674458063926645329 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Self-convolution equals A246570.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f.: A(x) = 1 + x + 7*x^2 + 51*x^3 + 425*x^4 + 3879*x^5 + 36527*x^6 +...

such that

A(x)^2 = 1/(1-x) + x/(1-x)^5 * (1 + 2^2*x + x^2)^2

+ x^2/(1-x)^9 * (1 + 4^2*x + 6^2*x^2 + 4^2*x^3 + x^4)^2

+ x^3/(1-x)^13 * (1 + 6^2*x + 15^2*x^2 + 20^2*x^3 + 15^2*x^4 + 6^2*x^5 + x^6)^2 +...

Explicitly,

A(x)^2 = 1 + 2*x + 15*x^2 + 116*x^3 + 1001*x^4 + 9322*x^5 + 89363*x^6 +...+ A246570(n)*x^n +...

PROG

(PARI) /* By definition: */

{a(n)=local(A=1); A = sqrt( sum(m=0, n, x^m/(1-x)^(4*m+1) * sum(k=0, 2*m, binomial(2*m, k)^2 * x^k)^2 +x*O(x^n)) ); polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A246563, A246570, A246571, A246573.

Sequence in context: A273055 A019472 A219306 * A230883 A304939 A293073

Adjacent sequences:  A246569 A246570 A246571 * A246573 A246574 A246575

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 30 2014

STATUS

approved

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Last modified June 13 11:17 EDT 2021. Contains 344990 sequences. (Running on oeis4.)